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.(2 points)
S.A.=
in.2
no offense but for u dum dums wondering the answer, its 543.
To find the surface area of a triangular prism, we need to calculate the areas of the three rectangular faces and the two triangular faces separately, and then add them together.
1. Calculate the area of the three rectangular faces:
Front and back faces:
Area = b * h = 17 inches * 9 inches = 153 square inches
Two side faces:
Area = l * h = 10 inches * 9 inches = 90 square inches
Total area of the three rectangular faces = 2 * 153 square inches + 2 * 90 square inches = 486 square inches
2. Calculate the area of the two triangular faces:
We need to calculate the area of one triangle and then multiply by 2 since both triangles are identical.
Area of a triangle = (1/2) * base * height
Area = (1/2) * s1 * l = (1/2) * 10 inches * 10 inches = 50 square inches
Total area of the two triangular faces = 2 * 50 square inches = 100 square inches
3. Finally, calculate the total surface area by adding the areas of the rectangular faces and the triangular faces:
Total Surface Area = 486 square inches + 100 square inches = 586 square inches
Therefore, the surface area of the display showcase is 586 square inches.