Question

What is the approximate sector area of a sector defined by minor arc overline CB m angle CAD=84^ BD=6 cm

Answer 1

The formula for the area of a sector of a circle is:

`A=(\theta)/(360)*\pi r^2`

We want to find the area of the blue sector.

First, let's find the angle of the sector. This angle and angle 84 are in a straight line. Thus, we can say:

`\theta+84=180`

Where θ is the angle of the sector.

Let's solve for θ:

`\begin{gathered} \theta+84=180 \\ \theta=180-84 \\ \theta=96 \end{gathered}`

We also recognize that BD is the diameter and BA is the radius.

We know

Radius is HALF of Diameter.

Given,

Diameter = 6

Radius = 6/2 = 3

Now, let's calculate the area of the sector:

`\begin{gathered} A=(\theta)/(360)*\pi r^2 \\ A=(96)/(360)*\pi(3)^2 \\ A=(4)/(15)*9\pi \\ A=(36\pi)/(15) \end{gathered}`

Rounded to 2 decimal places,

Answer

Area = 7.54 sq. cm.