How to find the area of this shape?

Question

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?

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Answer 1 · 2018-02-12T10:02:58

See below...

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

Secondly , the area of the square is $18 * 18= 324cm^2$

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 $(degrees *pi)/180$

$therefore$ the angle in radians is $(30 * pi)/180 = pi/6$

Now the area of a sector is equal to $1/2 * radius^2 * angle$

Where the angle is in radians.

Here the radius of the semi circles is $18cm$

$therefore$ 1 sector area is $1/2 * 18^2 * pi/6 = 27pi cm^2$

As we have two sectors we have another $27pi cm^2$

$therefore$ total area $= 324 + 27pi + 27pi = 493.646...cm^2$

$approx 493.65 cm^2$ to 2d.p