Question

Find the area of each figure. Round to the nearest tenth if necessary.

A quarter-circle with a diameter of 4 meters

Short answer

The area of the circle is $3.1{\mathrm{m}}^2$.

Step-by-step solution

Step 1. Given information.

A quarter circle with diameter 4 meters.

Step 2. Concept used.

Area of a quarter circle with radius r is given by $A=\frac{\pi r^2}{4}$.

Step 3. Calculations.

Since the radius is half of the diameter, so, the radius of the quarter circle is 2 meters.

$$\begin{gathered} A=\frac{\pi r^2}{4} \\ =\frac{3.14\times 2^2}{4} \\ =\frac{3.14\times 4}{4} \\ =3.14{\mathrm{m}}^2 \end{gathered}$$

Rounding off to the nearest tenth, we get,

$A=3.1{\mathrm{m}}^2$

Thus, the area of the quarter circle is $3.1{\mathrm{m}}^2$.