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 areas of all the individual faces and add them up.
Rectangular prism:
- Top and bottom faces: 20 cm x 13 cm = 260 cm^2 (2 faces)
- Front and back faces: 20 cm x 12 cm = 240 cm^2 (2 faces)
- Left and right faces: 13 cm x 12 cm = 156 cm^2 (2 faces)
Total surface area of the rectangular prism = 260 + 260 + 240 + 240 + 156 + 156 = 1,312 cm^2
Triangular prisms:
The formula for the surface area of a triangular prism is:
(Triangle Area x 2) + (Base Perimeter x Height)
Each triangular prism has an isosceles triangle face and a rectangular face.
Isosceles triangle face:
Area = 1/2 * base * height
Area = 1/2 * 13 cm * 5 cm = 32.5 cm^2
Base Perimeter = 2 x 8 cm + 13 cm = 16 cm + 13 cm = 29 cm
Surface Area of one triangular prism = (32.5 x 2) + (29 x 12) = 65 + 348 = 413 cm^2
Total surface area of both triangular prisms = 413 + 413 = 826 cm^2
Total surface area of the figure = 1,312 cm^2 + 826 cm^2 = 2,138 cm^2
So, the correct answer is not listed, but the closest option is 1,400 square centimeters.