Step-by-step explanation:
use a little imagination.
the whole thing is a combination of churches and half- circles.
and you know the formula for the area of a circle ?
A = pi×r²
so, the only difficulty is to find the circles and then the radius of each involved circle.
when you look at the picture, the shaded area is almost identical to the lower half of the main circle.
2 bumps "look" over into the other side, but one equally sized bump is removed from this lower half.
so, as a first step we will calculate the area of the lower half of the main circle.
the diameter is 24 m, so the radius is half of that : 12m
the area of the large circle is therefore
pi×12² = 144×pi m²
since we only need the (lower) half, we divide this by 2 :
144×pi / 2 = 72×pi m²
the bumps up and down are actually half-circles too. just of smaller circles.
since AB = BC = CD, we know each of these lines are 1/3 of the main diameter AD.
so, the diameter of the smaller circles is 24/3 = 8 m
and their radius is half of that = 8/2 = 4m
the area of such a small circle is therefore
As = pi×4² = 16×pi m²
and a small half-circle area is then
16×pi / 2 = 8×pi m²
so, for the full shaded area I need to take the large half-circle and add 2 small half-circles, and then subtract 1 small half-circle.
so, in total I only need to add 1 small half-circle.
Ashaded = 72×pi + 8×pi = 80×pi m²
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