Question

Surface Area Unit Test

8 of 168 of 16 Items

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
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Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the surface area of the triangular prism, we need to calculate the area of each face and then sum them up.

1. The area of the triangular base:
Area = 1/2 * base * height
Area = 1/2 * 27.9 * 5.1
Area = 71.145 cm2

2. The area of the other triangular face:
This face is identical to the base, so the area is also 71.145 cm2

3. The area of the three rectangular faces:
We need to find the dimensions of the three rectangles. The height of the triangular prism is 30.5 cm.
The length of the two rectangles will be equal to the base of the triangular face, so 27.9 cm.
The width of the rectangle will be the same as the perpendicular side of the triangular face, so 5.1 cm.

Area of one rectangle = length * width
Area of one rectangle = 27.9 * 5.1
Area of one rectangle = 142.29 cm2

There are 3 rectangular faces, so the total area of the rectangular faces is 3 * 142.29 = 426.87 cm2

Total Surface Area = 71.145 + 71.145 + 426.87
Total Surface Area = 569.16 cm2

Therefore, the amount of wrapping paper needed to wrap the toy is 569 cm2.