Answer:
Step-by-step explanation:
You can break the entire figure into two semi-circles, two triangles, and a rectangle.
The area of a semi-circle is 1/2 the area of a full circle. The area of a circle is πr^2. The area of the semi-circle is therefore:
[tex]\pi r^2/2=\pi (10^2)/2=50\pi[/tex]
The other semi-circle also contributes a value of 50π.
Moving on to the triangle, we must use Pythagorean's Theorem to find the value of the base:
[tex]a^2+b^2=c^2[/tex]
[tex]11^2+b^2=20^2[/tex]
[tex]121+b^2=400[/tex]
[tex]b^2=279[/tex]
[tex]b=\sqrt{279}[/tex]
The area of a triangle is:
[tex]Area=b*h/2[/tex]
[tex]A=(\sqrt{279} *11)/2[/tex]
The other triangle also contributes the same area.
Finally, the rectangle. To find the length of the rectangle, we must subtract the base of the triangle from 22. The length is:
[tex]l=22-\sqrt{279}[/tex]
The area of a rectangle is:
[tex]Area=l*w[/tex]
[tex]A=(22-\sqrt{279} )*(11)[/tex]
The total area of the figure is:
[tex]Area=2*(50\pi) +2*(\sqrt{279} *11/2)+11*(22-\sqrt{279} )[/tex]
[tex]Area=100\pi +11*\sqrt{279} +11*(22-\sqrt{279} )[/tex]
[tex]Area=100\pi +242[/tex]
[tex]Area=556.2[/tex]
