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 point).
S.A.=_ in.2
First, we need to find the area of the triangular bases. The formula for the area of a triangle is A = 1/2 * base * height. In this case, the base (b) and height (h) values given are for the triangle at the top of the prism.
Using the formula:
A = 1/2 * b * h
A = 1/2 * 17 * 9
A = 1/2 * 153
A = 76.5 square inches
Since there are two triangular bases on a triangular prism, we multiply this area by 2:
Total base area = 76.5 * 2
Total base area = 153 square inches
Next, we need to find the area of the three rectangular faces. The formula for the area of a rectangle is A = length * width. In this case, we have three faces with the following dimensions: s1 = 10 inches, s2 = 12 inches, s3 = 17 inches, and l = 10 inches.
Calculating the area of each face:
Face 1 = s1 * l = 10 * 10 = 100 square inches
Face 2 = s2 * l = 12 * 10 = 120 square inches
Face 3 = s3 * l = 17 * 10 = 170 square inches
Adding up the areas of the three rectangular faces:
Total face area = 100 + 120 + 170
Total face area = 390 square inches
Finally, we add up the total base area and total face area to find the total surface area of the display showcase:
S.A. = Total base area + Total face area
S.A. = 153 + 390
S.A. = 543 square inches
Therefore, the surface area of the display showcase is 543 square inches.