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

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

Answer 2

Answer: 5.43 square inches

Step-by-step 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 = $\frac{72}{360}\pi (6)^2$

= $\frac{2592\pi}{360}$

= $\frac{8138.88}{360}$

= $22.608$  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.