Find the area of the shaded region.

Mathematics

1 answer:

Iteru [2.4K]3 years ago

4 0

Keeping in mind that the area of a rectangle is simply width * length, if we get the area of the larger rectangle, and then subtract the area of the smaller rectangle, we're in effect making a hole in the larger rectangle's area and thus what's leftover is the shaded area.

$\bf \stackrel{\textit{area of the larger rectangle}}{(2x+2)(3x-4)}~~-~~\stackrel{\textit{area of the smaller rectangle}}{(x-3)(x-6)}
\\\\\\
\stackrel{FOIL}{6x^2-2x-8}~~~~-\stackrel{FOIL}{(x^2-9x+18)}\implies 6x^2-2x-8-x^2+9x-18
\\\\\\
5x^2+7x-26$

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This right triangular prism has a base with an area of 15 square feet. The height of the prism is 7 feet. What is V, the volume

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