Question

find the surface area of each figure. (use π = 3.14) 1) image of a composite solid with dimensions: 13 ft, 12 ft (height of triangle), 10 ft (base of triangle), 19 ft (length of rectangular prism), 9 ft (width), 11 ft (height) surface area = ___

Explanation:

Step1: Calculate surface area of the rectangular prism

The formula for the surface area of a rectangular prism is \( SA_{prism} = 2(lw + lh + wh) \), where \( l = 19 \) ft, \( w = 9 \) ft, \( h = 11 \) ft. But we need to adjust for the area where the triangular prism is attached (subtract the area of the two rectangles that are covered, and add the lateral faces of the triangular prism). First, calculate the full surface area of the rectangular prism:
\( SA_{prism\_full} = 2(19\times9 + 19\times11 + 9\times11) \)
\( = 2(171 + 209 + 99) \)
\( = 2(479) = 958 \) square feet.

Now, the area covered by the triangular prism on the top face of the rectangular prism: the length of the covered part is 10 ft (base of the triangle), so the area of the two rectangles (front and back? Wait, no, the top face of the rectangular prism has a length of 19 ft, and we have a triangular prism attached with base 10 ft. So the area we need to subtract from the top and bottom? Wait, no, the figure is a combination: a rectangular prism with a triangular prism on top. So the surface area of the composite figure is: surface area of rectangular prism - 2*(area of the rectangle where the triangle is attached) + lateral surface area of the triangular prism.

The area of the rectangle where the triangle is attached: length 10 ft, width 9 ft (since the width of the rectangular prism is 9 ft). So we subtract 2*(10*9) from the rectangular prism's surface area (because the top and bottom faces of the rectangular prism have a 10x9 area covered by the triangular prism, so we remove those two areas).

Then, the lateral surface area of the triangular prism: the triangular prism has two triangular faces (but wait, no, in the composite figure, the triangular faces are internal? Wait, no, looking at the diagram: the triangular prism has a triangular base with base 10 ft, height 12 ft, and the other sides of the triangle are 13 ft. The length of the triangular prism is 9 ft (same as the width of the rectangular prism). Wait, maybe I misread. Wait, the rectangular prism has length 19 ft, width 9 ft, height 11 ft. The triangular prism is on top, with base 10 ft (along the length of the rectangular prism), height 12 ft, and the slant sides 13 ft, and the length of the triangular prism is 9 ft (same as the width of the rectangular prism).

So the lateral surface area of the triangular prism: the two rectangular faces (the ones with sides 13 ft and 9 ft) and the rectangular face with side 10 ft and 9 ft? Wait, no. Wait, the triangular prism has three rectangular faces: two with dimensions 13 ft (the equal sides of the isoceles triangle) and 9 ft (the length of the prism), and one with dimensions 10 ft (the base of the triangle) and 9 ft (the length of the prism). But in the composite figure, the face where the triangular prism is attached to the rectangular prism (the base of the triangle, 10 ft by 9 ft) is internal, so we don't include that. So the lateral surface area of the triangular prism to add is 2*(13*9) + (10*9)? Wait, no, no. Wait, the surface area of the composite figure:

1. Surface area of rectangular prism: calculate all faces, then subtract the area of the two rectangles (top and bottom) where the triangular prism is attached (since those areas are now internal and not part of the surface). Wait, no, the top face of the rectangular prism has a length of 19 ft and width 9 ft. The triangular prism is attached on a part of the top face with length 10 ft and width 9 ft. So the top face of the rectangular prism now has an area of (19*9 - 10*9) + area of the triangular prism's top? No, maybe better to break it down:

- Front and back faces of the rectangular prism: each is 19*11, two of them: 2*19*11 = 418
- Right and left faces of the rectangular prism: each is 9*11, two of them: 2*9*11 = 198
- Bottom face of the rectangular prism: 19*9 = 171
- Top face of the rectangular prism: (19*9 - 10*9) = 9*(19-10) = 9*9 = 81 (wait, no, 19-10 is 9? Wait, 19 ft is the total length, 10 ft is the length of the triangular base. So the top face of the rectangular prism is divided into two parts: the part not covered by the triangular prism (length 19-10 = 9 ft, width 9 ft) and the part covered (length 10 ft, width 9 ft). But the covered part is internal, so we remove that, and add the lateral faces of the triangular prism.

Now, the triangular prism:

- The two triangular faces: area of each triangle is \( \frac{1}{2} \times 10 \times 12 = 60 \), two of them: 120. But wait, are these faces exposed? Looking at the diagram, the triangular faces are on the front and back? Wait, the diagram shows the triangular prism with a height of 12 ft (the altitude of the triangle) and the slant sides 13 ft. The length of the triangular prism is 9 ft (same as the width of the rectangular prism). So the front face of the triangular prism is the triangle (base 10 ft, height 12 ft), and the back face is also a triangle. Then, the lateral faces of the triangular prism are the three rectangles: two with dimensions 13 ft (the equal sides of the triangle) and 9 ft (length of prism), and one with dimensions 10 ft (base of triangle) and 9 ft (length of prism). But the rectangle with dimensions 10 ft and 9 ft is attached to the rectangular prism, so it's internal, so we don't include that. So the lateral surface area of the triangular prism to add is 2*(13*9) = 234.

Wait, maybe I made a mistake. Let's re-express the composite figure:

The figure is a rectangular prism (length 19, width 9, height 11) with a triangular prism (base triangle: base 10, height 12, sides 13; length 9) attached on top.

So the surface area is:

- Surface area of rectangular prism: \( 2(lw + lh + wh) = 2(19*9 + 19*11 + 9*11) = 2(171 + 209 + 99) = 2(479) = 958 \)
- Subtract the area of the two rectangles (top and bottom) where the triangular prism is attached: the area of each rectangle is 10*9, so two of them: 2*10*9 = 180. So 958 - 180 = 778
- Add the lateral surface area of the triangular prism: the triangular prism has two rectangular faces (each 13*9) and the two triangular faces? Wait, no, the triangular faces: are they exposed? Looking at the diagram, the front face of the composite figure has the front face of the rectangular prism (19*11) and the front face of the triangular prism (the triangle with base 10, height 12). Wait, no, the length of the rectangular prism is 19, and the triangular prism is attached on a 10 ft length. So the front face: the rectangular prism's front face is 19*11, but the triangular prism is attached on a 10 ft length, so the front face of the composite figure is the area of the rectangular prism's front face minus the area of the rectangle covered by the triangular prism (10*11) plus the area of the triangular face (10*12/2). Wait, this is getting confusing. Maybe a better approach:

Break down the composite figure into parts:

1. Rectangular prism: length \( l = 19 \) ft, width \( w = 9 \) ft, height \( h = 11 \) ft.

2. Triangular prism: base triangle with base \( b = 10 \) ft, height \( h_{triangle} = 12 \) ft, equal sides \( s = 13 \) ft, length (same as width of rectangular prism) \( L = 9 \) ft.

Now, the surface area of the composite figure is:

- Surface area of rectangular prism - 2*(area of the rectangle where triangular prism is attached) + lateral surface area of triangular prism + area of the two triangular faces (if exposed).

Wait, the area where the triangular prism is attached to the rectangular prism is a rectangle with dimensions \( b = 10 \) ft (base of triangle) and \( w = 9 \) ft (width of rectangular prism). So we have two such rectangles (top and bottom of the rectangular prism), so we subtract \( 2 \times (10 \times 9) \) from the rectangular prism's surface area.

Then, the lateral surface area of the triangular prism: the triangular prism has three rectangular faces: two with dimensions \( s = 13 \) ft and \( L = 9 \) ft, and one with dimensions \( b = 10 \) ft and \( L = 9 \) ft. But the one with \( b \) and \( L \) is attached to the rectangular prism, so we don't include that. So lateral surface area of triangular prism is \( 2 \times (13 \times 9) = 234 \) square feet.

Additionally, the two triangular faces of the triangular prism: each has area \( \frac{1}{2} \times 10 \times 12 = 60 \), so two of them: \( 2 \times 60 = 120 \) square feet. Wait, but are these triangular faces exposed? Looking at the diagram, the triangular prism is on top of the rectangular prism, so the front and back faces of the triangular prism (the triangles) are exposed, while the bottom face (the rectangle 10x9) is attached to the rectangular prism.

Now, let's recalculate the rectangular prism's surface area:

\( SA_{prism} = 2(lw + lh + wh) = 2(19*9 + 19*11 + 9*11) = 2(171 + 209 + 99) = 2(479) = 958 \)

Subtract the two rectangles (top and bottom) where the triangular prism is attached: \( 2*(10*9) = 180 \), so \( 958 - 180 = 778 \)

Add the lateral surface area of the triangular prism (the two 13x9 rectangles): \( 234 \)

Add the area of the two triangular faces: \( 120 \)

Wait, but also, the top face of the rectangular prism: originally, the top face is 19*9, but we subtracted 10*9 (the area covered by the triangular prism's bottom face). But the triangular prism's top face? No, the triangular prism's top face is a rectangle? Wait, no, the triangular prism has a triangular base, so its lateral faces are rectangles, and the two bases are triangles.

Wait, maybe I messed up the components. Let's look at the diagram again: the figure has a rectangular prism (length 19, width 9, height 11) with a triangular prism (base triangle: base 10, height 12, sides 13; length 9) attached on top. So the surface area includes:

- All faces of the rectangular prism except the part where the triangular prism is attached (top and bottom? No, only the top, because the bottom is a single face). Wait, no, the rectangular prism has 6 faces: top, bottom, front, back, left, right.

- The triangular prism has 5 faces? No, a triangular prism has 2 triangular bases and 3 rectangular lateral faces.

In the composite figure:

- The bottom face of the rectangular prism: 19*9 (exposed)
- The front face of the rectangular prism: 19*11 (exposed)
- The back face of the rectangular prism: 19*11 (exposed)
- The left face of the rectangular prism: 9*11 (exposed)
- The right face of the rectangular prism: 9*11 (exposed)
- The top face of the rectangular prism: (19*9 - 10*9) = 9*9 = 81 (exposed, because the triangular prism is attached on a 10*9 area)
- The two triangular faces of the triangular prism: each is (1/2)*10*12 = 60, so 2*60 = 120 (exposed, front and back)
- The two rectangular lateral faces of the triangular prism: each is 13*9, so 2*13*9 = 234 (exposed, the slanted sides)
- The rectangular lateral face of the triangular prism: 10*9 (attached to the rectangular prism, not exposed)

Now, let's sum all exposed areas:

- Bottom: 19*9 = 171
- Front: 19*11 = 209
- Back: 19*11 = 209
- Left: 9*11 = 99
- Right: 9*11 = 99
- Top (rectangular prism): 81
- Triangular faces: 120
- Triangular prism lateral faces (13*9): 234

Now, sum these up:

171 + 209 + 209 + 99 + 99 + 81 + 120 + 234

Calculate step by step:

171 + 209 = 380

380 + 209 = 589

589 + 99 = 688

688 + 99 = 787

787 + 81 = 868

868 + 120 = 988

988 + 234 = 1222

Wait, that can't be right. Let's check again.

Wait, maybe the front face of the composite figure is the front face of the rectangular prism (19*11) minus the area of the rectangle covered by the triangular prism (10*11) plus the area of the triangular face (10*12/2). Let's try that approach.

Front face: (19*11 - 10*11) + (1/2)*10*12 = (9*11) + 60 = 99 + 60 = 159

Back face: same as front: 159

Top face: (19*9 - 10*9) + (10*9)? No, no. Wait, the top face of the rectangular prism is 19*9, but the triangular prism is attached on a 10*9 area, so the exposed top area of the rectangular prism is 19*9 - 10*9 = 9*9 = 81. The top of the triangular prism: is it a rectangle? No, the triangular prism's top is a line? No, the triangular prism has length 9, so the top face of the triangular prism is a rectangle with length 9 and width equal to the length of the triangle's base? No, the triangular prism's lateral faces are rectangles with length 9 (the length of the prism) and width equal to the sides of the triangle.

Wait, I think the correct way is:

The composite figure is a rectangular prism with a triangular prism on top. The surface area is:

Surface area of rectangular prism + surface area of triangular prism - 2*(area of the base of the triangular prism)

Because the base of the triangular prism is attached to the rectangular prism, so we subtract twice that area (once from the rectangular prism, once from the triangular prism).

Surface area of rectangular prism: \( 2(lw + lh + wh) = 2(19*9 + 19*11 + 9*11) = 958 \)

Surface area of triangular prism: \( 2*(1/2)*b*h_{triangle} + (b + 2s)*L = b*h_{triangle} + (b + 2s)*L \) (where \( b = 10 \), \( h_{triangle} = 12 \), \( s = 13 \), \( L = 9 \))

So \( 10*12 + (10 + 2*13)*9 = 120 + (10 + 26)*9 = 120 + 36*9 = 120 + 324 = 444 \)

Now, subtract 2*(area of the base of the triangular prism) = 2*(10*9) = 180

So total surface area: 958 + 444 - 180 = 958 + 264 = 1222

Yes, that matches the previous calculation. So

Answer:

Step1: Calculate surface area of the rectangular prism

The formula for the surface area of a rectangular prism is \( SA_{prism} = 2(lw + lh + wh) \), where \( l = 19 \) ft, \( w = 9 \) ft, \( h = 11 \) ft. But we need to adjust for the area where the triangular prism is attached (subtract the area of the two rectangles that are covered, and add the lateral faces of the triangular prism). First, calculate the full surface area of the rectangular prism:
\( SA_{prism\_full} = 2(19\times9 + 19\times11 + 9\times11) \)
\( = 2(171 + 209 + 99) \)
\( = 2(479) = 958 \) square feet.

Now, the area covered by the triangular prism on the top face of the rectangular prism: the length of the covered part is 10 ft (base of the triangle), so the area of the two rectangles (front and back? Wait, no, the top face of the rectangular prism has a length of 19 ft, and we have a triangular prism attached with base 10 ft. So the area we need to subtract from the top and bottom? Wait, no, the figure is a combination: a rectangular prism with a triangular prism on top. So the surface area of the composite figure is: surface area of rectangular prism - 2*(area of the rectangle where the triangle is attached) + lateral surface area of the triangular prism.

The area of the rectangle where the triangle is attached: length 10 ft, width 9 ft (since the width of the rectangular prism is 9 ft). So we subtract 2(109) from the rectangular prism's surface area (because the top and bottom faces of the rectangular prism have a 10x9 area covered by the triangular prism, so we remove those two areas).

Then, the lateral surface area of the triangular prism: the triangular prism has two triangular faces (but wait, no, in the composite figure, the triangular faces are internal? Wait, no, looking at the diagram: the triangular prism has a triangular base with base 10 ft, height 12 ft, and the other sides of the triangle are 13 ft. The length of the triangular prism is 9 ft (same as the width of the rectangular prism). Wait, maybe I misread. Wait, the rectangular prism has length 19 ft, width 9 ft, height 11 ft. The triangular prism is on top, with base 10 ft (along the length of the rectangular prism), height 12 ft, and the slant sides 13 ft, and the length of the triangular prism is 9 ft (same as the width of the rectangular prism).

So the lateral surface area of the triangular prism: the two rectangular faces (the ones with sides 13 ft and 9 ft) and the rectangular face with side 10 ft and 9 ft? Wait, no. Wait, the triangular prism has three rectangular faces: two with dimensions 13 ft (the equal sides of the isoceles triangle) and 9 ft (the length of the prism), and one with dimensions 10 ft (the base of the triangle) and 9 ft (the length of the prism). But in the composite figure, the face where the triangular prism is attached to the rectangular prism (the base of the triangle, 10 ft by 9 ft) is internal, so we don't include that. So the lateral surface area of the triangular prism to add is 2(139) + (10*9)? Wait, no, no. Wait, the surface area of the composite figure:

1. Surface area of rectangular prism: calculate all faces, then subtract the area of the two rectangles (top and bottom) where the triangular prism is attached (since those areas are now internal and not part of the surface). Wait, no, the top face of the rectangular prism has a length of 19 ft and width 9 ft. The triangular prism is attached on a part of the top face with length 10 ft and width 9 ft. So the top face of the rectangular prism now has an area of (199 - 109) + area of the triangular prism's top? No, maybe better to break it down:

• Front and back faces of the rectangular prism: each is 1911, two of them: 219*11 = 418
• Right and left faces of the rectangular prism: each is 911, two of them: 29*11 = 198
• Bottom face of the rectangular prism: 19*9 = 171
• Top face of the rectangular prism: (199 - 109) = 9(19-10) = 99 = 81 (wait, no, 19-10 is 9? Wait, 19 ft is the total length, 10 ft is the length of the triangular base. So the top face of the rectangular prism is divided into two parts: the part not covered by the triangular prism (length 19-10 = 9 ft, width 9 ft) and the part covered (length 10 ft, width 9 ft). But the covered part is internal, so we remove that, and add the lateral faces of the triangular prism.

Now, the triangular prism:

• The two triangular faces: area of each triangle is \( \frac{1}{2} \times 10 \times 12 = 60 \), two of them: 120. But wait, are these faces exposed? Looking at the diagram, the triangular faces are on the front and back? Wait, the diagram shows the triangular prism with a height of 12 ft (the altitude of the triangle) and the slant sides 13 ft. The length of the triangular prism is 9 ft (same as the width of the rectangular prism). So the front face of the triangular prism is the triangle (base 10 ft, height 12 ft), and the back face is also a triangle. Then, the lateral faces of the triangular prism are the three rectangles: two with dimensions 13 ft (the equal sides of the triangle) and 9 ft (length of prism), and one with dimensions 10 ft (base of triangle) and 9 ft (length of prism). But the rectangle with dimensions 10 ft and 9 ft is attached to the rectangular prism, so it's internal, so we don't include that. So the lateral surface area of the triangular prism to add is 2(139) = 234.

Wait, maybe I made a mistake. Let's re-express the composite figure:

The figure is a rectangular prism (length 19, width 9, height 11) with a triangular prism (base triangle: base 10, height 12, sides 13; length 9) attached on top.

So the surface area is:

• Surface area of rectangular prism: \( 2(lw + lh + wh) = 2(199 + 1911 + 9*11) = 2(171 + 209 + 99) = 2(479) = 958 \)
• Subtract the area of the two rectangles (top and bottom) where the triangular prism is attached: the area of each rectangle is 109, so two of them: 210*9 = 180. So 958 - 180 = 778
• Add the lateral surface area of the triangular prism: the triangular prism has two rectangular faces (each 139) and the two triangular faces? Wait, no, the triangular faces: are they exposed? Looking at the diagram, the front face of the composite figure has the front face of the rectangular prism (1911) and the front face of the triangular prism (the triangle with base 10, height 12). Wait, no, the length of the rectangular prism is 19, and the triangular prism is attached on a 10 ft length. So the front face: the rectangular prism's front face is 1911, but the triangular prism is attached on a 10 ft length, so the front face of the composite figure is the area of the rectangular prism's front face minus the area of the rectangle covered by the triangular prism (1011) plus the area of the triangular face (10*12/2). Wait, this is getting confusing. Maybe a better approach:

Break down the composite figure into parts:

1. Rectangular prism: length \( l = 19 \) ft, width \( w = 9 \) ft, height \( h = 11 \) ft.

1. Triangular prism: base triangle with base \( b = 10 \) ft, height \( h_{triangle} = 12 \) ft, equal sides \( s = 13 \) ft, length (same as width of rectangular prism) \( L = 9 \) ft.

Now, the surface area of the composite figure is:

• Surface area of rectangular prism - 2*(area of the rectangle where triangular prism is attached) + lateral surface area of triangular prism + area of the two triangular faces (if exposed).

Wait, the area where the triangular prism is attached to the rectangular prism is a rectangle with dimensions \( b = 10 \) ft (base of triangle) and \( w = 9 \) ft (width of rectangular prism). So we have two such rectangles (top and bottom of the rectangular prism), so we subtract \( 2 \times (10 \times 9) \) from the rectangular prism's surface area.

Then, the lateral surface area of the triangular prism: the triangular prism has three rectangular faces: two with dimensions \( s = 13 \) ft and \( L = 9 \) ft, and one with dimensions \( b = 10 \) ft and \( L = 9 \) ft. But the one with \( b \) and \( L \) is attached to the rectangular prism, so we don't include that. So lateral surface area of triangular prism is \( 2 \times (13 \times 9) = 234 \) square feet.

Additionally, the two triangular faces of the triangular prism: each has area \( \frac{1}{2} \times 10 \times 12 = 60 \), so two of them: \( 2 \times 60 = 120 \) square feet. Wait, but are these triangular faces exposed? Looking at the diagram, the triangular prism is on top of the rectangular prism, so the front and back faces of the triangular prism (the triangles) are exposed, while the bottom face (the rectangle 10x9) is attached to the rectangular prism.

Now, let's recalculate the rectangular prism's surface area:

\( SA_{prism} = 2(lw + lh + wh) = 2(199 + 1911 + 9*11) = 2(171 + 209 + 99) = 2(479) = 958 \)

Subtract the two rectangles (top and bottom) where the triangular prism is attached: \( 2(109) = 180 \), so \( 958 - 180 = 778 \)

Add the lateral surface area of the triangular prism (the two 13x9 rectangles): \( 234 \)

Add the area of the two triangular faces: \( 120 \)

Wait, but also, the top face of the rectangular prism: originally, the top face is 199, but we subtracted 109 (the area covered by the triangular prism's bottom face). But the triangular prism's top face? No, the triangular prism's top face is a rectangle? Wait, no, the triangular prism has a triangular base, so its lateral faces are rectangles, and the two bases are triangles.

Wait, maybe I messed up the components. Let's look at the diagram again: the figure has a rectangular prism (length 19, width 9, height 11) with a triangular prism (base triangle: base 10, height 12, sides 13; length 9) attached on top. So the surface area includes:

• All faces of the rectangular prism except the part where the triangular prism is attached (top and bottom? No, only the top, because the bottom is a single face). Wait, no, the rectangular prism has 6 faces: top, bottom, front, back, left, right.

• The triangular prism has 5 faces? No, a triangular prism has 2 triangular bases and 3 rectangular lateral faces.

In the composite figure:

• The bottom face of the rectangular prism: 19*9 (exposed)
• The front face of the rectangular prism: 19*11 (exposed)
• The back face of the rectangular prism: 19*11 (exposed)
• The left face of the rectangular prism: 9*11 (exposed)
• The right face of the rectangular prism: 9*11 (exposed)
• The top face of the rectangular prism: (199 - 109) = 99 = 81 (exposed, because the triangular prism is attached on a 109 area)
• The two triangular faces of the triangular prism: each is (1/2)1012 = 60, so 2*60 = 120 (exposed, front and back)
• The two rectangular lateral faces of the triangular prism: each is 139, so 213*9 = 234 (exposed, the slanted sides)
• The rectangular lateral face of the triangular prism: 10*9 (attached to the rectangular prism, not exposed)

Now, let's sum all exposed areas:

• Bottom: 19*9 = 171
• Front: 19*11 = 209
• Back: 19*11 = 209
• Left: 9*11 = 99
• Right: 9*11 = 99
• Top (rectangular prism): 81
• Triangular faces: 120
• Triangular prism lateral faces (13*9): 234

Now, sum these up:

171 + 209 + 209 + 99 + 99 + 81 + 120 + 234

Calculate step by step:

171 + 209 = 380

380 + 209 = 589

589 + 99 = 688

688 + 99 = 787

787 + 81 = 868

868 + 120 = 988

988 + 234 = 1222

Wait, that can't be right. Let's check again.

Wait, maybe the front face of the composite figure is the front face of the rectangular prism (1911) minus the area of the rectangle covered by the triangular prism (1011) plus the area of the triangular face (10*12/2). Let's try that approach.

Front face: (1911 - 1011) + (1/2)1012 = (9*11) + 60 = 99 + 60 = 159

Back face: same as front: 159

Top face: (199 - 109) + (109)? No, no. Wait, the top face of the rectangular prism is 199, but the triangular prism is attached on a 109 area, so the exposed top area of the rectangular prism is 199 - 109 = 99 = 81. The top of the triangular prism: is it a rectangle? No, the triangular prism's top is a line? No, the triangular prism has length 9, so the top face of the triangular prism is a rectangle with length 9 and width equal to the length of the triangle's base? No, the triangular prism's lateral faces are rectangles with length 9 (the length of the prism) and width equal to the sides of the triangle.

Wait, I think the correct way is:

The composite figure is a rectangular prism with a triangular prism on top. The surface area is:

Surface area of rectangular prism + surface area of triangular prism - 2*(area of the base of the triangular prism)

Because the base of the triangular prism is attached to the rectangular prism, so we subtract twice that area (once from the rectangular prism, once from the triangular prism).

Surface area of rectangular prism: \( 2(lw + lh + wh) = 2(199 + 1911 + 9*11) = 958 \)

Surface area of triangular prism: \( 2(1/2)bh_{triangle} + (b + 2s)L = bh_{triangle} + (b + 2s)L \) (where \( b = 10 \), \( h_{triangle} = 12 \), \( s = 13 \), \( L = 9 \))

So \( 1012 + (10 + 213)9 = 120 + (10 + 26)9 = 120 + 36*9 = 120 + 324 = 444 \)

Now, subtract 2(area of the base of the triangular prism) = 2(10*9) = 180

So total surface area: 958 + 444 - 180 = 958 + 264 = 1222

Yes, that matches the previous calculation. So