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Answer :
Final answer:
The surface area of the triangular prism with the given dimensions is found by calculating the area of the three rectangles and two triangular faces and adding them together, giving a total of 160 square inches.
Explanation:
When you want to find the surface area of this triangular prism, you must calculate the area of all its faces and then sum them up. This specific triangular prism has given dimensions: a base of 8 inches, a width of 2 inches, a height of 6 inches, and a slanting height of 10 inches.
First, calculate the area of the three rectangular faces. The base times the height will give the area of the two identical rectangles (8 inches x 6 inches = 48 square inches each), and the base times the width will give the area of the bottom rectangle (8 inches x 2 inches = 16 square inches).
Now, calculate the area of the two triangular faces. The formula for the area of a triangle is (1/2) × base × height. Here, the base is 8 inches and the height is 6 inches.
Area of one triangle = (1/2) × 8 inches × 6 inches = 24 square inches. Since there are two triangles, multiply this by 2 to get 48 square inches.
Summing up the areas of all faces:
- Area of two rectangular faces: 48 sq in + 48 sq in = 96 sq in
- Area of the bottom rectangle: 16 sq in
- Area of two triangular faces: 24 sq in + 24 sq in = 48 sq in
Total surface area = 96 sq in + 16 sq in + 48 sq in = 160 sq in.
Therefore, the surface area of the shape is 160 square inches.
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