Question

Examine the composite figure formed by placing a triangular prism on top of a rectangular prism. All of the measurements have centimeters as their units.

The triangular base has height 12, base 14 & 2 other sides 13 & 15. The prism height is 20. The rectangular prism is 8 by 14 by 20. The prisms share a face that is 14 by 20.


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To find the surface area, Brad splits the figure into two pieces, the rectangular prism and the triangular prism.


He finds the total surface area of the rectangular prism by finding the area of each face to get 1,104 cm2.

He then finds the total surface area of the triangular prism by finding the area of each face to get 1,008 cm2.

Finally, he adds the surface areas together to get 2,112 cm2.

Is Brad's solution correct? Why or why not?

Answer 1

Answer:90x567

Explanation:

Answer 2

Explanation:

Brad's solution to find the surface area of the composite figure is not correct.

In his solution, Brad adds the surface areas of the triangular prism and the rectangular prism separately,

but it's not taking into account that the two prisms share a face that is 14 by 20.

When finding the surface area of a composite figure, it's important to take into account any shared faces.

Since the two prisms share a face that is 14 by 20, Brad should subtract this area from one of the prisms,

otherwise he will be counting it twice in the final result.

The correct method would be:

Rectangular prism: (2 * 8 * 14) + (2 * 14 * 20) + (2 * 8 * 20) = 1,104 cm^2

Triangular prism: (1/2 * 14 * 12) + (1/2 * 13 * 15) + (3 * 14 * 20) = 1,008 cm^2

Subtracting shared area: 1,104 cm^2 + 1,008 cm^2 - (14 * 20) = 2,096 cm^2.

So Brad's solution is incorrect, the correct surface area of the composite figure is 2,096 cm^2.