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 h=9 b=17 s1=10 s2=12 s3=17 and l=10 inches
The surface area of a triangular prism can be calculated using the formula:
Surface Area = 2(base area) + (perimeter of base) x height
First, calculate the base area:
Base area = (1/2)bh
Base area = (1/2)(17)(9) = 76.5 square inches
Next, calculate the perimeter of the base:
Perimeter = s1 + s2 + s3
Perimeter = 10 + 12 + 17 = 39 inches
Now, calculate the surface area:
Surface Area = 2(76.5) + (39)(10)
Surface Area = 153 + 390
Surface Area = 543 square inches
Therefore, the surface area of the display showcase is 543 square inches.