Surface Area Unit Test

Question

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Question
Use the image to answer the question.

An illustration shows a 3 D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 30.5 centimeters and 27.9 centimeters. The perpendicular side of the triangular face measures 5.1 centimeter and the hypotenuse measures 28.4 centimeter.

A toy came in a container that is shaped like a triangular prism. How much wrapping paper is needed to wrap the toy? Round your answer to the nearest whole number.

(1 point)
S.A. =
cm2

Answer 1

First, we need to calculate the surface area of the triangular prism.

The formula for the surface area of a triangular prism is:
S.A. = 2(base area) + (perimeter of base) * height

For the triangular base, the base area is:
1/2 * base * perpendicular side
= 1/2 * 27.9 * 5.1
= 71.145 cm²

The perimeter of the base is the sum of all of its edges:
perimeter = 27.9 + 5.1 + 28.4
= 61.4 cm

Now we can substitute these values into the formula:
S.A. = 2(71.145) + 61.4 * 30.5
= 142.29 + 1872.7
= 2015 cm²

Therefore, you would need 2015 cm² of wrapping paper to wrap the toy. Rounding to the nearest whole number, the answer is 2015 cm².