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 amount of wrapping paper needed, we need to find the total surface area of the triangular prism.
The surface area of a triangular prism is calculated by adding the areas of the two triangular faces and the three rectangular faces.
1. Calculate the area of the two triangular faces:
Area = 1/2 * base * height
Area = 1/2 * 27.9 cm * 5.1 cm = 71.145 square cm
Total area of both triangular faces = 2 * 71.145 square cm = 142.29 square cm
2. Calculate the area of the three rectangular faces:
Length of the triangular prism = 30.5 cm
Height of the triangular prism = 5.1 cm
Area of rectangular face = length * height
Area of rectangular faces = 3 * (30.5 cm * 5.1 cm) = 463.05 square cm
3. Add the areas of the triangular faces and rectangular faces to get the total surface area:
Total surface area = 142.29 square cm + 463.05 square cm = 605.34 square cm
Therefore, approximately 605 square centimeters of wrapping paper is needed to wrap the toy.