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What is the volume of this prism? All angles are right angles.

What is the volume of this prism? All angles are right angles.-example-1

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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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