Question

A rectangular pyramid and a rectangular prism have bases of the same dimensions as shown below.
http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_0700_Subtest_03_15/image0034e5fb4df.jpg
The surface area of the rectangular pyramid is 146 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?

320 in2

336 in2

292 in2

438 in2

Answer 1

A quick exercise in geometrical reasoning, I like it!
Anyways, If we contract the face, we are subtracting the top face, and contracting half of every side face, while retaining the base as a normal, so our formula turns to be:\[A_s'=\frac{A_s-2B}{2}+B=\frac{A_s}{2}\]Where A' is the surface area of our rectangular pyramid and A is the surface area of our rectangle. So, we turn it into:
\[2A_s'=A_s\]And we are done. Our answer is\[292\text{ in}^2\]