Question

Find the total surface are of the triangular prism to the nearest tenth.

Answer 1

The prism's surface area is option 2. 145.3 ft².

Step-by-step explanation:

Step 1; To calculate the triangular prism's surface area, we calculate the areas of all the 5 sides. We divide the prism into 2 triangles and 3 rectangles, find the area individually and then sum them all up in order to determine the area of the entire triangular prism.

Step 2; There are two triangles with base lengths of 9.8 ft and heights of 5.33 feet. To calculate a triangle's area we multiply $\frac{1}{2}$ with the product of the base length and it's height.

Area of 1 triangle = $\frac{1}{2}$  × 9.8 × 5.33 = 26.117 ft²

Area of both triangles = Area of 1 triangle × 2 = 26.117 × 2 = 52.234 ft².

Step 3; There are three rectangles with a common width of 3.8 feet but there are three different lengths. Any rectangle's area is calculated by multiplying the rectangle's length with its width.

Area of rectangle with length 9.8 ft = 9.8 × 3.8 = 37.24 ft².

Area of rectangle with length 8.5 ft = 8.5 × 3.8 = 32.3 ft².

Area of rectangle with length 6.2 ft = 6.2 × 3.8 = 23.56 ft².

Step 4; The area of the entire triangular prism = Area of 2 triangles + Area of all the 3 rectangles.

= 52.234 + 37.24 + 32.3 + 23.56 = 145.334 ft². By rounding the calculated value to the nearest tenth we get the area as 145.3 ft².