Find the area between two shapes Geometry

The area of the circle with radius r equals:

A=\pi r^2

Since r=2, we have:

A=4\pi

Now consider the area of the non-colored shape. We can see that it is an isosceles right triangle with a side length of 4, which is the diameter of the circle. Thus the area of the non-colored area is:

A' = \dfrac{1}{2} \times 2 \times 4=4

So the area of the colored area is:

The area of the parallelogram with base a and height h equals:

A=ah

Here, the base is:

a=AB = CD = 6

And:

h= MH = 4

Therefore, the area of the parallelogram is:

A= ah= 6 \times 4 = 24

Now consider the area of the non-colored shape, which is a triangle. The area of the triangle equals:

A' = \dfrac{1}{2} \times MH \times AB

A' = \dfrac{1}{2} \times 4 \times 6 = 12

So the area of the colored area is:

The area of the circle with radius r equals:

A=\pi r^2

Since r=5, we have:

A=25\pi

The area of the colored area is:

A' = 8 \times 6 = 48

So the area of the colored area is:

The area of the rectangle equals:

A=4 \times 8 = 32

The area of the circle with radius r equals:

A'=\pi r^2

Since r=2, we have:

A'=4\pi

So the area of the colored area is:

The area of the rectangle equals:

A= 4 \times 12 = 48

Now consider the area of the non-colored shape. We can see that it is a rhombus whose diagonals have lengths of 4 and 12. Thus the area of the non-colored area is:

A' = \dfrac{1}{2} \times 4 \times 12 = 24

So the area of the colored area is:

The area of the circle with radius r equals:

A=\pi r^2

Since r=2, we have:

A=4\pi

Now consider the area of the non-colored shape. We can see that it is a square of side a. A side of the square can be calculated by the Pythagoras theorem:

a=\sqrt{2^2 +2^2} =\sqrt{8}

Thus the area of the square equals:

A'=a^2 = \left(\sqrt{8}\right)^2 = 8

So the area of the colored area is:

The area of the circle with radius r equals:

A=\pi r^2

Since r=5, we have:

A=25\pi

Now consider the area of the non-colored shape. We can see that it is a trapezoid. The bases are 8 and 10 and the height is 3. Thus the area of the non-colored shape is:

A' = \dfrac{1}{2}\left(8+10\right) \times 3 = 27

So the area of the colored area is: