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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To find the surface area of the triangular prism, we need to calculate the area of each face and then add them together.
1. Area of the triangular face:
Area = 0.5 * base * height
Area = 0.5 * 27.9 cm * 5.1 cm
Area = 0.5 * 142.29 cm
Area = 71.145 cm2
2. Area of the rectangular faces:
There are 3 rectangular faces on a triangular prism.
Each rectangular face has the same area, which is equal to the base times the length of the prism.
Area = base * length
Area = 27.9 cm * 30.5 cm
Area = 850.95 cm2
(There are three rectangular faces, so total area = 850.95 cm2 * 3 = 2552.85 cm2)
Total Surface Area = 71.145 cm2 (triangular face) + 2552.85 cm2 (rectangular faces) = 2623 cm2
Therefore, approximately 2623 cm2 of wrapping paper is needed to wrap the toy.