Question

find the area. use 3.14 or a calculator button for pi and provide an answer accurate to the nearest tenth.

Explanation:

Step1: Identify sector formula

The figure is a 90° (right angle) sector of a circle. The formula for the area of a sector with central angle $\theta$ (in degrees) and radius $r$ is $A = \frac{\theta}{360^\circ} \times \pi r^2$. Here, $\theta = 90^\circ$, $r = 16$ ft.

Step2: Substitute values into formula

$$ A = \frac{90^\circ}{360^\circ} \times \pi \times (16)^2 $$

Simplify $\frac{90^\circ}{360^\circ} = \frac{1}{4}$, and $16^2 = 256$:

$$ A = \frac{1}{4} \times \pi \times 256 $$

Step3: Calculate intermediate value

$$ \frac{1}{4} \times 256 = 64 $$

So $A = 64\pi$

Step4: Compute numerical value

Use $\pi = 3.14$:

$$ A = 64 \times 3.14 = 200.96 $$

Step5: Round to nearest tenth

$200.96$ rounded to the nearest tenth is $201.0$

Answer:

$201.0$ square feet