Question

1. find the surface area:

6 ft
8 ft
7.5 ft
10 ft
(color this answer black)

Explanation:

This is a triangular prism. The surface area of a triangular prism is the sum of the areas of the two triangular bases and the three rectangular lateral faces.

Step 1: Area of the triangular bases

The triangle is a right triangle with legs 6 ft and 8 ft. The area of a triangle is $\frac{1}{2} \times base \times height$.
So, area of one triangle: $\frac{1}{2} \times 6 \times 8 = 24$ square feet.
Since there are two triangular bases, total area of triangles: $2 \times 24 = 48$ square feet.

Step 2: Area of the rectangular lateral faces

• The first rectangle has dimensions 6 ft (leg of triangle) and 7.5 ft (height of prism). Area: $6 \times 7.5 = 45$ square feet.
• The second rectangle has dimensions 8 ft (leg of triangle) and 7.5 ft (height of prism). Area: $8 \times 7.5 = 60$ square feet.
• The third rectangle has dimensions 10 ft (hypotenuse of triangle) and 7.5 ft (height of prism). Area: $10 \times 7.5 = 75$ square feet.

Step 3: Total surface area

Sum the areas of the triangular bases and the rectangular lateral faces: $48 + 45 + 60 + 75 = 228$ square feet.

Answer:

The surface area of the triangular prism is $\boxed{228}$ square feet.