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
To find the surface area of the triangular prism, we need to calculate the area of each face and then add them all together.
First, we find the area of the triangular bases:
Area of one triangular base = (1/2)bh = (1/2)(17)(9) = 76.5 in^2
Since there are two triangular bases, the total area of the triangular bases = 2(76.5) = 153 in^2
Next, we find the area of the three rectangular faces:
Area of rectangular face #1 = 10 * 9 = 90 in^2
Area of rectangular face #2 = 17 * 9 = 153 in^2
Area of rectangular face #3 = 10 * 17 = 170 in^2
Now, we add up all the areas to find the total surface area:
Total surface area = 153 + 90 + 153 + 170 = 566 in^2
Therefore, the surface area of Christian's display showcase is 566 square inches.