Question

The figure below shows a polygon $ABCDEFGH,$ consisting of rectangles and right triangles. When cut out and folded on the dotted lines, the polygon forms a triangular prism. Suppose that:

$AH = EF = 8$

and

$GH = 14.$

What is the volume of the prism?

$112$

$128$

$192$

$240$

$288$

Solution:

When the net is folded, the matching side lengths give $GF=EF=8$ . Since $GFCB$ is a rectangle, $BC=8$ . The fold identifies $AB$ with $BC$ , so $AB=8$ . In rectangle $HJBA$ , this gives $HJ=8$ , and the opposite side $BJ$ equals $AH=8$ .

Since $GH=14$ , we have $GJ=14-8=6$ . Thus one triangular base of the prism is right triangle $BJG$ , with area $\frac{6\cdot8}{2}=24.$ The prism length is $GF=8$ , so the volume is $24\cdot8=192$ .

Thus, the correct answer is C.

2022 AMC 8 Problem 24

Solution:

Problem 24 in Other Years