help with geometry

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

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.