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
To find the surface area of the triangular prism, we need to calculate the area of each face and then add them together.
1. The base of the triangular prism is a right triangle with lengths of 30.5 cm and 27.9 cm. The area of this triangle is 0.5 * base * height = 0.5 * 30.5 * 27.9 = 425.175 cm².
2. Since there are two triangular faces with the same dimensions, the total area of the triangular faces is 2 * 425.175 = 850.35 cm².
3. The rectangular face of the prism is a rectangle with dimensions of 30.5 cm by 5.1 cm. The area of this rectangle is length * width = 30.5 * 5.1 = 155.55 cm².
4. Since there are two rectangular faces with the same dimensions, the total area of the rectangular faces is 2 * 155.55 = 311.1 cm².
5. The total surface area of the prism is the sum of the areas of the triangular and rectangular faces, which is 850.35 + 311.1 = 1161.45 cm².
Therefore, approximately 1161 cm² of wrapping paper is needed to wrap the toy.