How to find the area of this shape?

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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?

1 Answer
Feb 12, 2018

Answer:

See below...

Explanation:

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