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)
Responses

296 in2

296 in. squared

432 in2

432 in. squared

220 in2

220 in. squared

300 in2

300 in. squared
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Answer 1

Surface area = 2·(area of trapezoid) + (perimeter of trapezoid)·(prism height).

Trapezoid area = ((4+10)/2)·4 = 7·4 = 28.
Leg = sqrt(((10−4)/2)^2 + 4^2) = sqrt(3^2+4^2) = 5.
Perimeter = 4+10+5+5 = 24.
Lateral area = 24·10 = 240.
Total surface area = 2·28 + 240 = 56 + 240 = 296 in^2.

Answer: 296 in^2.