Question

Calculate the area of the following figure correct to 2 decimal places if can show or explain work

Answer 1

The way we approach a question like this, is by looking at what portion of the circle we actually have to calculate the area of. We know that a circle is a shape that goes 360 degrees around a point. Therefore we know that, for example, a semicircle, or half a circle, would cover half the amount of degrees. This is important, because as well as covering half the number of degrees, it also covers half the area. For the figure in your picture, we are told that the portion missing from the circle is 90 degrees (shown by the right angle symbol in the center).
this means that 90 degrees worth of the circle is missing, so if we do 360÷90, we find that the answer equals$\frac{3}{4}$. This means that we are dealing with $\frac{3}{4}$ of a circle. So, we simply find the area of the circle normally, and then multiply by $\frac{3}{4}$:
The formula for area of a circle is $\pi r^{2}$, so in this case, it can be said to be $\pi (10^{2} )$, which is equal to 314.15
Now we simply take that area and multiply it by the fraction we established earlier:
314.15 x $\frac{3}{4}$ = 235.61
Therefore the area of the figure is 235.61 $cm^{2}$
I hope this helped and please remember to try and not only understand the answer, but the maths that worked it out too :))