Krishna
0

METHOD 1:

Step 1: Set up a formula for the area of the sector.

NOTE: Area of the sector = (\frac{l}{2\pi r}) \pi r^2

Area of the sector  =   \frac{lr}{2}  (Simplified)

Where, r = the length of the radius, and l = the length of the arc.

Step 2: Substitute the arc length and radius into the formula.

Area of the sector  =   \frac{lr}{2}

Area of the sector  = \frac{3 * 5 \pi }{2}

Step 3: Simplify the values to know the sector area.

METHOD 2:

Step 1: Calculate the central angle by using the arc length formula

Skill 1: Write the arc length formula

Arc length = \theta * radius

\theta = Central angle

Skill 2: Substitute the known values in the formula.

5 \pi = \theta * 3

Skill 3: Solve for central angle

5 \pi = \theta * 3

\frac{5 \pi}{3} = \theta

Step 2: Set up a formula for the sector area

NOTE: A ratio will need to be constructed. Recall that a circle is composed

of 360 degrees. Therefore, the following ratio can be made,

\frac{\theta}{360} = \frac{\text{sector area} (A_C)}{\text{Total area} (A_T)}

Sector area = \frac{\theta}{360} * \pi r^2 (since area = \pi r^2)

where, \theta = Central angle.

Step 3: Plug the sector’s central angle measurement into the formula.

Step 4: Plug the sector’s radius measurement into the formula.

Step 5: Solve for the area:

EXAMPLE: Sector area = \frac{\theta}{360} * \pi r^2 (since area = \pi r^2)

Sector area = \frac{60}{360}*\left(3.14\right)\left(5\right)^2

Sector area = 13.09 cm^2