Find the total surface area of a triangular prism with a height of 12cm the width of 12cm and the base of 12cm
To find the total surface area of a triangular prism, we first need to find the area of the three faces of the prism (two triangular faces and one rectangular face) and then add them together.
First, let's calculate the area of the triangular faces:
1. The base of the triangle is 12cm and the height is also 12cm. The formula to calculate the area of a triangle is A = 1/2 * base * height. So, for one triangular face:
A = 1/2 * 12cm * 12cm = 72 square cm
Since there are two triangular faces, the total area of both triangular faces would be 2 * 72 = 144 square cm
Next, let's calculate the area of the rectangular face:
1. The width (which is also the base of the triangle) is 12cm and the height of the prism is 12cm. The formula to calculate the area of a rectangle is A = length * width. So, for the rectangular face:
A = 12cm * 12cm = 144 square cm
Now, let's add up the areas of all three faces to find the total surface area of the triangular prism:
Total surface area = 144 (two triangular faces) + 144 (rectangular face) = 288 square cm
Therefore, the total surface area of the triangular prism is 288 square cm.