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)
To calculate the amount of wrapping paper needed, we need to find the surface area of the triangular prism.
First, calculate the area of the triangular face:
Area = (1/2) * base * height
Area = (1/2) * 27.9 * 5.1
Area = 71.145 cm²
Next, calculate the area of the rectangular faces:
- There are two rectangular faces with the dimensions 30.5 cm x 5.1 cm.
Area = length * width
Area = 30.5 * 5.1
Area = 155.55 cm²
Now, calculate the total surface area of the triangular prism:
Total surface area = 2(Area of triangular face) + 2(Area of rectangular face)
Total surface area = 2(71.145) + 2(155.55)
Total surface area = 142.29 + 311.1
Total surface area = 453.39 cm²
Therefore, approximately 453 cm² of wrapping paper is needed to wrap the toy.