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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S.A. = 528 cm2
To find the surface area of a triangular prism, we need to find the area of each face and then add them up.
1. Area of the triangular base:
Area = (1/2) x base x height
Area = (1/2) x 27.9 cm x 5.1 cm
Area = 71.145 cm2
2. Area of the two rectangular sides:
Area = perimeter of triangular base x height
Perimeter = 27.9 cm + 30.5 cm + 28.4 cm
Perimeter = 86.8 cm
Area = 86.8 cm x 5.1 cm
Area = 442.68 cm2
Adding up the areas of the base and the two sides:
Total Surface Area = 71.145 cm2 + 442.68 cm2 + 442.68 cm2
Total Surface Area = 528.425 cm2
Rounded to the nearest whole number:
S.A. ≈ 528 cm2
Therefore, 528 cm2 of wrapping paper is needed to wrap the toy.