A triangular prism has a height of 1.5 inches and right triangular bases with a height of 1.5 inches, length of 5 inches, and a hypotenuse measuring 5.22 inches. What is the prism's surface area?
To find the surface area of a triangular prism, we need to find the lateral surface area and the area of the two triangular bases.
Lateral Surface Area:
The lateral surface area of a triangular prism is equal to the perimeter of the base triangle multiplied by the height of the prism.
Perimeter of base triangle = 5 + 5.22 + 5 = 15.22 inches
Height of the prism = 1.5 inches
Lateral Surface Area = 15.22 * 1.5 = 22.83 square inches
Area of Triangular Bases:
Area of a triangle = 0.5 * base * height
Area of triangular base = 0.5 * 5 * 1.5 = 3.75 square inches
Total Surface Area:
Total Surface Area = Lateral Surface Area + 2 * Area of Triangular Bases
Total Surface Area = 22.83 + 2(3.75) = 22.83 + 7.5 = 30.33 square inches
Therefore, the surface area of the triangular prism is 30.33 square inches.