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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To find the surface area of the triangular prism, first calculate the surface area of the triangular face:
Area = 1/2 * base * height
Area = 1/2 * 27.9 cm * 5.1 cm
Area = 71.145 cm2
Now, calculate the surface area of the three rectangular faces:
1. Face with base 30.5 cm and height 5.1 cm:
Area = 30.5 cm * 5.1 cm
Area = 155.55 cm2
2. Face with base 30.5 cm and height 27.9 cm:
Area = 30.5 cm * 27.9 cm
Area = 850.95 cm2
3. Face with base 27.9 cm and height 5.1 cm:
Area = 27.9 cm * 5.1 cm
Area = 142.29 cm2
Now, add up all the areas to find the total surface area:
71.145 cm2 (triangular face) + 155.55 cm2 + 850.95 cm2 + 142.29 cm2 = 1220.94 cm2
Therefore, approximately 1221 cm2 of wrapping paper is needed to wrap the toy.