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
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.