Given:
The given figure consists of a rectangle, a semicircle and another semicircle removed from it.
The length of the rectangle = 15 unit
The width of the rectangle = 10 unit
The diameter of the semicircle = 10 unit
So, the radius of the semicircle = 5 unit
To find the formula of given fig.
Formula:
The area of the given fig is
[tex]A = A_{1} +A_{2}-A_{3}[/tex]
where,
[tex]A_{1}[/tex] be the area of the rectangle
[tex]A_{2}[/tex] be the area of the semicircle
[tex]A_{3}[/tex] be the area of the semi circle that needs to remove
Area of the rectangle [tex]A_{1} = lb[/tex], where, l be the length and b be the width
The area of the semicircle [tex]A_{2}[/tex] = [tex]\frac{1}{2}\pi r^{2}[/tex]
The area of the semicircle [tex]A_{3}[/tex] = [tex]\frac{1}{2}\pi r^{2}[/tex]
where, r be the radius.
Now,
Putting, l=15 and b = 10 we get,
[tex]A_{1} = (15)(10)[/tex] sq unit
[tex]A_{1} = 150[/tex] sq unit
Putting, r = 5 and π = 3.14 we get,
[tex]A_{2} = \frac{1}{2} (3.14)(5^{2} )[/tex] sq unit
[tex]A_{2} = 39.25[/tex] sq unit
Similarly, [tex]A_{3} = 39.25[/tex] sq unit
Therefore,
The area of the given figure = (150+39.25-39.25) sq unit
= 150 sq unit
Hence,
The area of the given figure is 150 sq unit.
