Question

find the surface area of each figur
1)
(figure of a triangular prism with side 5 yd, 5 yd, height 10 yd)
surface area: ______

Explanation:

Step1: Identify the figure (triangular prism)

The figure is a triangular prism with a right - angled triangular base (legs of 5 yd each) and height (length of the prism) 10 yd.

Step2: Find the area of the triangular bases

The formula for the area of a right - angled triangle is $A=\frac{1}{2}\times base\times height$. For the triangular base, base = 5 yd and height = 5 yd. So the area of one triangular base is $\frac{1}{2}\times5\times5=\frac{25}{2}=12.5$ square yards. Since there are two triangular bases, the total area of the two bases is $2\times12.5 = 25$ square yards.

Step3: Find the area of the rectangular faces

• There are three rectangular faces. Two of them have dimensions 5 yd (width) and 10 yd (length), and one has dimensions (hypotenuse of the triangle) and 10 yd. First, find the hypotenuse of the right - angled triangle using the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$, where $a = 5$ and $b = 5$. So $c=\sqrt{5^{2}+5^{2}}=\sqrt{25 + 25}=\sqrt{50}=5\sqrt{2}\approx7.07$ yd. But wait, maybe I made a mistake. Wait, looking at the figure, maybe the triangular base is an isosceles right triangle, and the three rectangular faces: two with sides 5 and 10, and one with sides (the hypotenuse) and 10? Wait, no, maybe the base is a right - angled triangle with legs 5 and 5, and the three rectangular faces: two rectangles with length [LLM SSE On Failure]

Answer:

Step1: Identify the figure (triangular prism)

The figure is a triangular prism with a right - angled triangular base (legs of 5 yd each) and height (length of the prism) 10 yd.

Step2: Find the area of the triangular bases

The formula for the area of a right - angled triangle is $A=\frac{1}{2}\times base\times height$. For the triangular base, base = 5 yd and height = 5 yd. So the area of one triangular base is $\frac{1}{2}\times5\times5=\frac{25}{2}=12.5$ square yards. Since there are two triangular bases, the total area of the two bases is $2\times12.5 = 25$ square yards.

Step3: Find the area of the rectangular faces

• There are three rectangular faces. Two of them have dimensions 5 yd (width) and 10 yd (length), and one has dimensions (hypotenuse of the triangle) and 10 yd. First, find the hypotenuse of the right - angled triangle using the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$, where $a = 5$ and $b = 5$. So $c=\sqrt{5^{2}+5^{2}}=\sqrt{25 + 25}=\sqrt{50}=5\sqrt{2}\approx7.07$ yd. But wait, maybe I made a mistake. Wait, looking at the figure, maybe the triangular base is an isosceles right triangle, and the three rectangular faces: two with sides 5 and 10, and one with sides (the hypotenuse) and 10? Wait, no, maybe the base is a right - angled triangle with legs 5 and 5, and the three rectangular faces: two rectangles with length [LLM SSE On Failure]