Question

Find the area of segment CED given the following information:

radius = 6in, area of ΔCAD = 17.18in2, and m∠CAD = 72°
Round your answer to the nearest hundredths if necessary.

Answer 1

Answer: 5.43 square inches

Explanation:

Here, the area of triangle ACD = 17.18 square inches,

And, the radius of the triangle having center A = 6 inches

The central angle of the arc CED = 72°

Hence, the area of the sector CAD =
`(72)/(360)\pi (6)^2`

=
`(2592\pi)/(360)`

=
`(8138.88)/(360)`

=
`22.608` square inches

Since, the area of CED = The area of sector CAD - Area of triangle ACD

= 22.608 - 17.18

= 5.428 ≈ 5.43 square inches.

Answer 2

Area of sector CAD = 72 / 360 x pi x 6^2 = 7.2pi = 22.6195 in^2

Therefore, area of segment CED = 22.6195 - 17.18 = 5.44 in^2