Question

Christian collectors model cars and planes. He has a display showcase of all of his collectors' items. Solve this real-world problem to find the surface area of the display showcase if it is the shape of a triangular prism with the following dimensions: h =9 inches, b =17 inches, s1 =10 inches, s2 =12 inches, s3 = 17 and l =10 inches.(1 point) S.A.= in.2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the surface area of a triangular prism, we need to find the areas of the three rectangles (sides) and the two triangles (top and bottom) that make up the shape.

Let's start by calculating the area of the three rectangles:
1. Area of side 1 = l x h = 10 x 9 = 90 square inches
2. Area of side 2 = b x h = 17 x 9 = 153 square inches
3. Area of side 3 = s3 x h = 17 x 9 = 153 square inches

Next, let's calculate the area of the two triangles:
1. Area of top triangle = (1/2) x b x s1 = (1/2) x 17 x 10 = 85 square inches
2. Area of bottom triangle = (1/2) x b x s2 = (1/2) x 17 x 12 = 102 square inches

Now, let's add up all the areas to find the total surface area:
S.A. = 90 + 153 + 153 + 85 + 102
S.A. = 583 square inches

Therefore, the surface area of the display showcase is 583 square inches.