Question

Find the area of the sector

Answer 1

Answer:

$\boxed {\boxed {\sf a \approx 190.9 \ yd^2}}$

Step-by-step explanation:

There are 2 formulas for the area of a sector, but since we are given the central angle in degrees (not radians), we will use this formula:

$a= \frac {\theta}{360} \times \pi r^2$

Where θ is the central angle and r is the radius.

For this circle, the radius is 9 yards and the central angle is 270 degrees. We can substitute these values into the formula.

$a= \frac {270}{360} \times \pi \times (9 \ yd )^2$

Solve the fraction.

$a=0.75 \times \pi \times (9 \ yd)^2$

Solve the exponent.

• (9 yd)²= 9 yd* 9 yd=81 yd²

$a= 0.75 \times \pi \times 81 \ yd^2$

Multiply all three numbers together.

$a= 190.851753706 \ yd^2$

The question asks us to round to the nearest tenth.

• 190.851753706

The 5 in the hundredth place tells us to round the 8 up to a 9.

$a \approx 190.9 \ yd^2$

The area of the sector is approximately 190.9 square yards.

Answer 2

Answer:

The easiest way to do this is to calculate the Area of the whole circle and then subtract the 1/4 of the missing piece.

So:

• A=pi×81
• and then pi×81/4
• and then pi×81-[pi×81/4]