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? (1 point)
To find the surface area of the triangular prism, we need to calculate the area of all the faces and then add them together.
1. Triangular Base:
Area = (1/2) * base * height
Area = (1/2) * 5 * 1.5
Area = 3.75 square inches
Since there are two triangular bases, the total area of the triangular bases is 2 * 3.75 = 7.5 square inches.
2. Rectangular Sides:
The height of the triangular prism is the same as the height of the triangular base, which is 1.5 inches. The length of the sides is equal to the hypotenuse of the triangular base, which is given as 5.22 inches.
Area = perimeter * height
Perimeter = sum of all 3 sides = 5 + 1.5 + 5.22 = 11.72 inches
Therefore, the area of each of the two rectangular sides is 11.72 * 1.5 = 17.58 square inches. Since there are two of these sides, the total area of the rectangular sides is 2 * 17.58 = 35.16 square inches.
Therefore, the total surface area of the triangular prism is:
7.5 (triangular bases) + 35.16 (rectangular sides) = 42.66 square inches
Therefore, the surface area of the triangular prism is 42.66 square inches.