Find the lateral surface area of the triangular prism. Solve this problem by determining the area of the shape’s net. (1 point) Responses 420 in.2 420 in. squared 564 in.2 564 in. squared 504 in.2 504 in. squared 480 in.2
To find the lateral surface area of a triangular prism, we need to find the area of the three rectangular faces that make up the prism's net.
First, we need to find the area of the two triangular faces. The formula for the area of a triangle is 1/2 * base * height.
Given that the base of the triangle is 14 inches and the height is 10 inches, the area of one triangle is:
1/2 * 14 in * 10 in = 70 in^2
Since there are two triangular faces, the total area of the two triangles is:
2 * 70 in^2 = 140 in^2
Next, we need to find the area of the three rectangular faces. The formula for the area of a rectangle is length * width.
The length of the prism is 14 inches and the width is 10 inches, so the area of one rectangle is:
14 in * 10 in = 140 in^2
Since there are three rectangular faces, the total area of the three rectangles is:
3 * 140 in^2 = 420 in^2
Finally, add the areas of the two triangles and three rectangles together to find the total lateral surface area of the triangular prism:
140 in^2 + 420 in^2 = 560 in^2
Therefore, the lateral surface area of the triangular prism is 560 in^2. The closest answer choice is 564 in^2.