Question

Find the area of a sector with a central angle of 7.2 radians and a radius of 14 units

Answer 1

Answer:

$\boxed {\boxed {\sf a= 705.6 \ units^2 }}$

Step-by-step explanation:

Since we are given the central angle in radians, we should use this formula for the sector area:

$a=\frac{1}{2}r^2 \theta$

where r is the radius and θ is the angle in radians.

The radius is 14 units and the angle is 7.2 radians.

$r= 14 \ units \\\theta= 7.2$

Substitute the values into the formula.

$a= \frac{1}{2} (14 \ units)^2 (7.2)$

Solve the exponent.

• (14 units)²= 14 units* 14 units =196 units²

$a=\frac{ 1}{2} (196 \ units^2)(7.2)$

$a=\frac{ 1}{2}(1411.2 \ units^2)$

Multiply by 1/2 or divide by 2.

$a= 705.6 \ units^2$

The area of the sector is 705.6 square units.