Determine the surface area of a prism with a triangular base. The base is an isosceles triangle with a base length of 12 in. and a height of 8 in. The height of the prism is 14 in.
To find the surface area of a prism with a triangular base, we need to find the area of the three faces and add them together.
1. The area of the triangular base can be found using the formula for the area of a triangle:
Area = 1/2 * base * height
Area = 1/2 * 12 * 8
Area = 48 square inches
2. The area of the two lateral faces can be found by multiplying the perimeter of the base by the height of the prism. Since the base is an isosceles triangle, we can find the perimeter by adding the base length (12 in.) with twice the length of one of the equal sides.
Perimeter = 12 + 2 * 12 = 36 inches
Area of two lateral faces = Perimeter * height = 36 * 14 = 504 square inches
3. The total surface area is the sum of the area of the base and the two lateral faces:
Total surface area = base area + 2 * lateral faces
Total surface area = 48 + 504
Total surface area = 552 square inches
Therefore, the surface area of the prism is 552 square inches.