Two same-sized triangular prisms are attached to a rectangular prism as shown.
If a = 20 cm, b = 13 cm, c = 12 cm, d = 5 cm, and e = 8 cm, what is the surface area of the figure?
(2 points)
Responses
1,004 square centimeters
1,004 square centimeters
1,400 square centimeters
1,400 square centimeters
1,592 square centimeters
1,592 square centimeters
1,208 square centimeters
To find the surface area of the figure, we need to calculate the surface areas of each individual shape and then add them together.
1. Surface area of the rectangular prism:
Surface area = 2(ab + ac + bc) = 2(20*13 + 20*12 + 13*12) = 2(260 + 240 + 156) = 2(656) = 1312 cm²
2. Surface area of one triangular prism:
Each triangular prism has 2 triangles and 3 rectangular sides.
Surface area = 2*(1/2 * e * b + 1/2 * e * c) + 3d*e
Surface area = 2*(1/2 * 8 * 13 + 1/2 * 8 * 12) + 3*5*8
Surface area = 2*(52 + 48) + 120
Surface area = 2*(100) + 120
Surface area = 200 + 120
Surface area = 320 cm²
3. Since there are two identical triangular prisms attached to the rectangular prism, the total surface area of the triangular prisms is 2*320 = 640 cm².
4. The total surface area of the figure is the sum of the surface area of the rectangular prism and the two triangular prisms:
Total surface area = 1312 + 640 = 1952 cm²
Therefore, the surface area of the figure is 1,952 square centimeters.