# How to find the area of this shape?

## I don't know how knowing the angles can help me solve this equation. If it is not a problem, could someone explain this to me?

Feb 12, 2018

See below...

#### Explanation:

Firstly, all of the lines with a dash are equal in length $\therefore 18 c m$

Secondly , the area of the square is $18 \cdot 18 = 324 c {m}^{2}$

To work out the area of the sectors, the most simplest way to do it is by using radians.

Radians are another form of measurement for angles.

1 radian happens when the radius is equal to the Arc length.

To convert to radians we do $\frac{\mathrm{de} g r e e s \cdot \pi}{180}$

$\therefore$ the angle in radians is $\frac{30 \cdot \pi}{180} = \frac{\pi}{6}$

Now the area of a sector is equal to $\frac{1}{2} \cdot r a \mathrm{di} u {s}^{2} \cdot \angle$

Where the angle is in radians.

Here the radius of the semi circles is $18 c m$

$\therefore$ 1 sector area is $\frac{1}{2} \cdot {18}^{2} \cdot \frac{\pi}{6} = 27 \pi c {m}^{2}$

As we have two sectors we have another $27 \pi c {m}^{2}$

$\therefore$ total area $= 324 + 27 \pi + 27 \pi = 493.646 \ldots c {m}^{2}$

$\approx 493.65 c {m}^{2}$ to 2d.p