To find the surface area of the triangular prism showcase, we need to calculate the surface areas of each individual face and add them all together.
The formula for the surface area of a triangular prism is:
Surface area = 2*(area of the base) + (perimeter of the base) * height
First, let's calculate the area of the base, which is a triangle with dimensions s1, s2, and s3:
Area of the base = 1/4 * √(s1 + s2 + s3) * (s1 + s2 + s3)
Area of the base = 1/4 * √(10 + 12 + 17) * (10 + 12 + 17)
Area of the base = 1/4 * √39 * 39
Area of the base = 1/4 * √1521
Area of the base = 1/4 * 39
Area of the base = 9.75 square inches
Next, let's calculate the perimeter of the base:
Perimeter of the base = s1 + s2 + s3
Perimeter of the base = 10 + 12 + 17
Perimeter of the base = 39 inches
Now, we can calculate the surface area of the triangular prism showcase:
Surface area = 2*(9.75) + (39)*9
Surface area = 19.5 + 351
Surface area = 370.5 square inches
Therefore, the surface area of Christian's display showcase is 370.5 square inches.
Christian collects 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 answer