Question

Find the area of segment CFD given the following information: radius = 8in, area of ΔCBD = 25.9in2, and m∠CBD = 54° Round your answer to the nearest hundredths if necessary.
A. 4.26 in2
B. 20.10 in2
C. 3.23 in2
D. 17.90 in2

Answer 1

Answer:

A. 4.26 in^2

Step-by-step explanation:

Step 1: Find the area of the sector DBC. Here we have to use the formula.

Area of a sector = Central Angle/360 *π$r^{2}$

The area of the sector DBC = (54/360)*3.14*$8^{2}$

= 30.16

Step 2: Area of segment CFD = Area of the sector DBC - Area of the ΔCBD

= 30.17 - 25.9

Area of segment CFD = 4.27in^2