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) Responses 24.75 in.2 24.75 in. squared 25.08 in.2 25.08 in. squared 30.33 in.2 30.33 in. squared 25.41 in.2
The surface area of a triangular prism can be calculated by finding the areas of the two triangular bases and the three rectangular sides and then adding them together.
The area of each triangular base can be found using the formula for the area of a triangle: 0.5 * base * height.
For one triangle:
Area = 0.5 * 5 * 1.5 = 3.75 square inches.
Since there are two triangular bases, the total area for both is 2 * 3.75 = 7.5 square inches.
Next, we need to find the area of the three rectangular sides. Two of the sides have a length of 5 inches (same as the base of the triangles) and a height of 1.5 inches. The other side is the hypotenuse of the triangles, which is 5.22 inches.
Total area for the three sides:
(2 * 5 * 1.5) + (5.22 * 1.5) = 15 + 7.83 = 22.83 square inches.
Finally, add the areas of the two triangular bases and the three rectangular sides to find the total surface area of the prism:
7.5 + 22.83 = 30.33 square inches.
Therefore, the prism's surface area is 30.33 in.2.