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.

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.

nonbinarycode · Answer

attachment

AZ · Answer

We only need to focus on the image on the left

The area that they want to find is what I shaded in red
|dw:1622683138685:dw|

AZ · Answer

angle CBD is 54 degrees

We need to first find the area of the entire segment that I shaded in blue|dw:1622683275773:dw|

The formula for that is

$\text{area} = \dfrac{\theta}{360}\times \pi r^2$

where $\theta$ is the angle of the segment which is 54 in our case

so can you find the area of the segment?

All you have to do is plug in 54 and the radius which they told us is 8

54/360 * pi * 8^2 = ??

AZ · Answer

after that, to find the shaded red area, you have to subtract the area of the triangle which they told us was 25.9

so subtract 25.9 from the number you just got and that will be your final answer
(that is, the area of the red shaded segment CFD)

nonbinarycode · Answer

thx

AZ · Answer

No problem