The surface area of the rectangular pyramid is 131 square inches. The height of the rectangular prism is the same as the slant height of the pyramid. What is the surface area of the rectangular prism

Question

pfenn1 · Answer

Is there a figure or drawing that goes along with this problem?

directrix · Answer

Is the rectangular base of the pyramid given to be congruent to the rectangular base of the prism?

anonymous · Answer

Directrix Yes it is .

directrix · Answer

Surface Area of Rectangular Pyramid
SA = (1/2)*p*L + B where p is the perimeter of the rectangular base, L is the slant height, and B is the area of the rectangular base. The surface area is given to be 131.
So, 131 = (1/2)*p*L + B  ----> Pyramid
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Surface Area of Rectangular Prism
SA = ph + 2B where p is the perimeter of the base, h is the height of the prism, and B is the area of the rectangular bases.
Note: the rectangular base of the pyramid is congruent to the rectangular base of the prism.
Also, the slant height of the pyramid is congruent to the height of the prism.
So, SA = p*L + B --> Prism
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Take the pyramid formula and compare it to that of the prism
131 = (1/2)*p*L + B ==> Multiply both sides by two ==>
2(131) = 2* [ (1/2)*p*L + B ], so
262 = p*L + 2B ==> the right side (p*L + 2B) is the algebraic expression for the surface area of the prism.
So, the surface area of the prism is 262 square inches.  --> Answer is 262

anonymous · Answer

Thanks^

directrix · Answer

Glad to help. Hope it is correct.