Question

A rectangular pyramid and a rectangular prism have bases of the same dimensions as shown below.

A rectangular pyramid and a rectangular prism are shown. Both have the length of the rectangular base equal to 8 inches and width of the base equal to 6 inches.

The surface area of the rectangular pyramid is 174 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?

234 in2

148 in2

254 in2

348 in2

Answer 1

Let the height of square prism is h
Surface area of square prism is
\[2(lb+lh+bh)\]
l=6
b=8

\[2(6*8+8*h+8*h)\rightarrow 96+16h+16h \]
so
\[96+16h+16h=174 \]
\[32h=78\]
so we get
\[h=2.4375\]
Do you understand this?

Answer 2

yes