Question

Find the area of the segment (shaded in blue in the figure) of a circle whose radius is 8 feet, formed by a central angle of  70^o.

[Hint: Subtract the area of the triangle from the area of the sector to obtain the area of the segment.]

Answer 1

 Step 1 :

Find the area of the segment.

Area of the segment = area of the sector area of the triangle.

Area of the sector : , where is in radians.

Radius of the circle .

Central angle .

 Step 2 :

Substitute corresponding values in .

Area of the sector is 39.104 square units.

 Step 3 :

Let the angle is and,

The two sides of the triangle are .      (Since radius of the circle )

Area of the triangle is .

Substitute corresponding values.

Area of the triangle is 30.07 square units.

Step 4 :

Area of the segment = area of the sector area of the triangle.

                              = 39.104 30.07

                              = 9.03.

Area of the segment is 9.03 square units.

Solution :

Area of the segment is 9.03 square units.