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.
To find the surface area of the triangular prism, we need to calculate the area of each face and add them together.
1. Area of the triangular face:
Base = 27.9 cm
Height = 5.1 cm
Area = 1/2 * base * height = 1/2 * 27.9 * 5.1 = 71.295 cm²
2. Area of the other rectangular faces:
Length = 30.5 cm
Width = 5.1 cm
Area = length * width = 30.5 * 5.1 = 155.55 cm²
There are two identical rectangular faces, so the total area for both is 2 * 155.55 = 311.1 cm²
Now, add the areas of the triangular face and the rectangular faces:
Total surface area = 311.1 + 71.295 = 382.395 cm²
Therefore, approximately 382 cm² of wrapping paper is needed to wrap the toy.