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# help with geometry

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find the approximate area of the shaded region

Mar 3, 2021

#1
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To find the diameter of the circle, we need to use the pythagorean theorem and use it on one of the triangles in the rectangle.

Pythagorean theorem: $$a^2+b^2=c^2$$

Lets replace a with 21 and b with 20 to get the equation $$21^2+20^2=c^2$$

Simplifying the left side gives us $$841=c^2$$

which means that $$c = \sqrt{841}$$ which is exactly $$29$$

Now that we know the diameter of the circle, we can find the area.

The formula for the area of a circle is $$𝜋r^2$$, r being the radius.

We can find the radius by dividing 29 by 2, 14.5
Using the formula, we get A ≈ 660.52

So the area of the circle is about 660.52

To find the area of the rectangle inside the circle, we multiply the length by the width.

21*20=420

Now we subtract 420 from 660.52

660.52-420 = 240.52

Mar 3, 2021
#2
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I agree with Swag :)

Just find the radius of the circle using the Pythagorean theorem, then use the formula pi*r^2 to find the area of the circle, and finally subtract the area of the rectangle from the circle.

Mar 3, 2021