Question

A base of a prism is an isosceles trapezoid that has one base length of 4 in., another base length of 10 in., and a height of 4 in. The height of the prism is 10 in. Which of the following correctly calculates the surface area of the prism with an isosceles trapezoid base?(1 point)

300 in2

432 in2

220 in2

296 in2

Which of the following correctly calculates the lateral area of a cylinder with a base radius length of 7 in. and a height of 10 in? Use π=3.14 .(1 point)

1,538.3 in.2

593.46 in.2

747.32 in.2

439.6 in.2


Peter plays renaissance drums, which are cylindrical in shape, in military reenactments in his hometown. He just bought a new drum with the money he has saved from working. Peter’s new drum has a diameter of 13 inches and a height of 19 inches. What is the approximate surface area of Peter’s drum?(1 point)

1,306.90 in.2

2,613.81 in.2

1,041.44 in.2

816.81 in.2
Which of the following formulas correctly calculates the surface area of a cone?(1 point)

2πrl+2πr2

πrl+2πr2

πrl+πr2

2πrl+πr2


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A rectangular pyramid has a base with sides 10 ft. and 7 ft. The slant height where the base has the longer side is 7 ft., and the slant height where the base has the shorter side is 8 ft. Which of the following correctly calculates the surface area of the pyramid?(1 point)

196 ft.2

70 ft.2

202 ft.2

126 ft.2

Answer 1

1) Surface area of prism = 2*(area of trapezoid) + (perimeter of trapezoid)*prism height.
- Area trapezoid = 0.5*(4+10)*4 = 28 → two bases = 56.
- Leg = sqrt((10-4)^2/4 + 4^2) = sqrt(3^2+4^2)=5, perimeter = 4+10+5+5=24.
- Lateral = 24*10 = 240. Total = 56+240 = 296 in^2.
Answer: 296 in^2.

2) Lateral area of cylinder = 2πrh = 2(3.14)(7)(10) = 439.6 in^2.
Answer: 439.6 in^2.

3) Surface area of Peter’s drum (closed cylinder) = 2πr^2 + 2πrh, r = 6.5, h = 19.
- Using π ≈ 3.1416 gives SA ≈ 1041.44 in^2.
Answer: 1,041.44 in^2.

4) Surface area of a cone = lateral + base = πrl + πr^2.
Answer: πrl + πr^2.

5) Surface area of pyramid = base area + lateral area.
- Base = 10*7 = 70.
- Two triangles with base 10: each 0.5*10*7 = 35 → total 70.
- Two triangles with base 7: each 0.5*7*8 = 28 → total 56.
- Lateral = 70+56 = 126. Total = 70+126 = 196 ft^2.
Answer: 196 ft^2.