Answer:
528 cubic inches
Explanation:
You want to know the volume of the L-shaped prism shown.
Base area
The area of the L-shaped face can be found a couple of ways. Drawing a diagonal line from the inside corner to the outside corner divides it into two congruent trapezoids with bases 12 in and 10 in, and height 2 in. The area of one such trapezoid is ...
A = 1/2(b1 +b2)h
A = (1/2)(12 in + 10 in)(2 in) = 22 in²
The area of the L-shaped face is then ...
base area = 2(22 in²) = 44 in²
Prism volume
As with all prisms, the volume is given by ...
V = Bh
where B is the area of the base, and h is the distance between bases.
V = (44 in²)(12 in) = 528 in³
The volume of the prism is 528 cubic inches.
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Additional comment
Another way to find the area of the L shape is to subtract the 10 in × 10 in cutout area from the 12 in × 12 in square that bounds that face.
12² - 10² = 144 -100 = 44 in²
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