Question
What is the total surface area of the triangular prism? square centimeters base 4 height 6
largest rectangle of the prism is 24
smallest rectangle of the prism is 24
the triangular base of the prism is 12
largest rectangle of the prism is 24
smallest rectangle of the prism is 24
the triangular base of the prism is 12
Answers
GPT 3.5
To find the total surface area of a triangular prism, you need to find the area of each individual face and then add them all together.
1. The two triangular bases of the prism:
Each triangular base has a base of 4 and a height of 6. The area of one triangular base is 1/2 * base * height = 1/2 * 4 * 6 = 12 square cm. Since there are two triangular bases, the total area of both bases is 2 * 12 = 24 square cm.
2. The three rectangular faces of the prism:
The largest rectangle has dimensions 12 by 4, so its area is 12 * 4 = 48 square cm.
The smallest rectangle has dimensions 6 by 4, so its area is 6 * 4 = 24 square cm.
Since there are three rectangular faces, the total area of all three rectangles is 48 + 24 + 24 = 96 square cm.
Therefore, the total surface area of the triangular prism is 24 (from the bases) + 96 (from the rectangles) = 120 square cm.
1. The two triangular bases of the prism:
Each triangular base has a base of 4 and a height of 6. The area of one triangular base is 1/2 * base * height = 1/2 * 4 * 6 = 12 square cm. Since there are two triangular bases, the total area of both bases is 2 * 12 = 24 square cm.
2. The three rectangular faces of the prism:
The largest rectangle has dimensions 12 by 4, so its area is 12 * 4 = 48 square cm.
The smallest rectangle has dimensions 6 by 4, so its area is 6 * 4 = 24 square cm.
Since there are three rectangular faces, the total area of all three rectangles is 48 + 24 + 24 = 96 square cm.
Therefore, the total surface area of the triangular prism is 24 (from the bases) + 96 (from the rectangles) = 120 square cm.