Question

C is the center of the circle. Find the area of the segment shown in the figure,

A Asegment = 28.50 u?
B. A segment = 66.00 u?
C. A segment = 78.50 02
D. A segment = 107.00 u?

Answer 1

Answer: A 28.50 sq. u

Explanation:

In the given figure , radius of the circle : r= 10 u

Central angle made by Arc ED:
`\theta`= 90° ( right angle )

Now , the area of the segment is given by :-

Area of segment = Area of sector (ECD) - Area of triangle(ECD) (i)

Formula : Area of right triangle = 0.5 x Base x Height

Area of sector =
`(\theta)/(360^(\circ))*\pi r^2`

Using above formulas in (i) and substituting corresponding values , we get

Area of segment =

`(90^(\circ))/(360^(\circ))*\pi (10)^2-0.5*10*10\\\\=(1)/(4)(3.14)(100)-50\\\\=78.5-50=28.5\ sq.u`

Hence, the correct answer is A 28.50 sq. u