Question

1. a base of a right prism whose height is 10 feet is shown. find the surface area of the prism.
2. a base of a right prism whose height is 10 inches is shown. find the surface area of the prism.
3. a base of a right prism whose height is 10 miles is shown. find the surface area of the prism.
4. a base of a right prism whose height is 10 kilometers is shown. find the surface area of the prism.
5. a base of a right prism whose height is 10 yards is shown. find the surface area of the prism.

Answer:

1. For the first prism (height \(h = 10\) feet):

• Step 1: Find the area of the base
• Split the base - shape into two rectangles. One rectangle has dimensions \(8\times7\) and the other has dimensions \((17 - 8)\times3=9\times3\).
• The area of the first rectangle \(A_1=8\times7 = 56\) square - feet.
• The area of the second rectangle \(A_2=9\times3 = 27\) square - feet.
• The area of the base \(B=A_1 + A_2=56+27 = 83\) square - feet.
• Step 2: Find the perimeter of the base
• The perimeter of the base \(P=(7 + 8+4 + 3+17)=39\) feet.
• Step 3: Calculate the surface area of the prism
• The surface - area formula of a prism is \(SA = 2B+Ph\).
• Substitute \(B = 83\), \(P = 39\), and \(h = 10\) into the formula:
• \(SA=2\times83+39\times10\)
• \(SA = 166+390\)
• \(SA = 556\) square feet.

1. For the second prism (height \(h = 10\) inches):

• Step 1: Find the area of the base
• Split the base into two rectangles. One rectangle has dimensions \(5\times7\) and the other has dimensions \((12 - 5)\times2 = 7\times2\).
• The area of the first rectangle \(A_1=5\times7 = 35\) square - inches.
• The area of the second rectangle \(A_2=7\times2 = 14\) square - inches.
• The area of the base \(B=A_1 + A_2=35 + 14=49\) square - inches.
• Step 2: Find the perimeter of the base
• The perimeter of the base \(P=(7 + 5+5 + 2+12)=31\) inches.
• Step 3: Calculate the surface area of the prism
• Using the formula \(SA = 2B+Ph\), substitute \(B = 49\), \(P = 31\), and \(h = 10\).
• \(SA=2\times49+31\times10\)
• \(SA = 98+310\)
• \(SA = 408\) square inches.

1. For the third prism (height \(h = 10\) miles):

• Step 1: Find the area of the base
• Split the base into two rectangles. One rectangle has dimensions \(4\times6\) and the other has dimensions \((12 - 4)\times2=8\times2\).
• The area of the first rectangle \(A_1=4\times6 = 24\) square - miles.
• The area of the second rectangle \(A_2=8\times2 = 16\) square - miles.
• The area of the base \(B=A_1 + A_2=24 + 16=40\) square - miles.
• Step 2: Find the perimeter of the base
• The perimeter of the base \(P=(6 + 4+4 + 2+12)=28\) miles.
• Step 3: Calculate the surface area of the prism
• Using the formula \(SA = 2B+Ph\), substitute \(B = 40\), \(P = 28\), and \(h = 10\).
• \(SA=2\times40+28\times10\)
• \(SA = 80+280\)
• \(SA = 360\) square miles.

1. For the fourth prism (height \(h = 10\) kilometers):

• Step 1: Find the area of the base
• Split the base into two rectangles. One rectangle has dimensions \(6\times12\) and the other has dimensions \((10 - 6)\times5 = 4\times5\).
• The area of the first rectangle \(A_1=6\times12 = 72\) square - kilometers.
• The area of the second rectangle \(A_2=4\times5 = 20\) square - kilometers.
• The area of the base \(B=A_1 + A_2=72 + 20=92\) square - kilometers.
• Step 2: Find the perimeter of the base
• The perimeter of the base \(P=(12 + 6+7 + 5+10)=40\) kilometers.
• Step 3: Calculate the surface area of the prism
• Using the formula \(SA = 2B+Ph\), substitute \(B = 92\), \(P = 40\), and \(h = 10\).
• \(SA=2\times92+40\times10\)
• \(SA = 184+400\)
• \(SA = 584\) square kilometers.

1. For the fifth prism (height \(h = 10\) yards):

• Step 1: Find the area of the base
• Split the base into two rectangles. One rectangle has dimensions \(6\times9\) and the other has dimensions \((13 - 6)\times3=7\times3\).
• The area of the first rectangle \(A_1=6\times9 = 54\) square - yards.
• The area of the second rectangle \(A_2=7\times3 = 21\) square - yards.
• The area of the base \(B=A_1 + A_2=54 + 21=75\) square - yards.
• Step 2: Find the perimeter of the base
• The perimeter of the base \(P=(9 + 6+6 + 3+13)=37\) yards.
• Step 3: Calculate the surface area of the prism
• Using the formula \(SA = 2B+Ph\), substitute \(B = 75\), \(P = 37\), and \(h = 10\).
• \(SA=2\times75+37\times10\)
• \(SA = 150+370\)
• \(SA = 520\) square yards.

1. Answer: 556 square feet
2. Answer: 408 square inches
3. Answer: 360 square miles
4. Answer: 584 square kilometers
5. Answer: 520 square yards