Find the area of the figure to the nearest tenth

Solution:

The diagram shown in the problem is part of a circle of radius 7 inches. The angle subtended at the center is 165°.

The area of the circle of radius 7 inches is given by the formula:

Area of circle radius r = πr²

Substituting r = 7 inches the area of the circle is 

A  = π(7)²  = 49 π inches²

A circle represents an angle of 360°. at the center. Therefore we can state that 360° corresponds to the area of the circle. Therefore 165°, which corresponds to the sector shown in the question, will correspond to an area of :

Area of the sector =  (165°/360°)  ×  49 π

= (11/24)49 π

= (539/24)π

=  22.46π  inches²

Area of the sector =  70.6  inches² 

Find the area of the figure to the nearest tenth

Summary:

The area of the figure to the nearest tenth is 70.6  inches²