Given:
A circle with a diameter of 20 m inside a triangle with a base length of 56 m and a height of 56 m.
To find:
The area of the shaded region.
Solution:
To find the area of the shaded region, we must subtract the area of the circle from the area of the triangle.
The area of a circle [tex]= \pi r^{2} .[/tex]
The diameter of the circle is 20 m so the radius is [tex]\frac{20}{2}=10[/tex] m.
The area of the circle [tex]= (3.14)(10^{2} )= (3.14)(100)= 314[/tex] square m.
The area of a triangle [tex]=\frac{1}{2}(b)(h).[/tex]
The triangle has a base length of 56 m and a height of 56 m.
The area of the triangle [tex]= \frac{1}{2}(56)(56) = \frac{1}{2} (3,136) = 1,568[/tex] square m.
The area of the shaded region [tex]=1,568-314 = 1,254[/tex] square m.
The area of the shaded region is 1,254 square m.
