area of the shaded region

Geometry Level pending

Find the area of the shaded region. If your answer can be expressed as $\dfrac{a}{b} \pi -c$ , where $a,b$ and $c$ are positive coprime integers, give $a+b+c$ .

Note: All arcs in the diagram are all circular sectors.

The answer is 100.

1 solution

A Former Brilliant Member
Oct 8, 2017

$A_s=\dfrac{1}{4}\pi(8^2)-\dfrac{1}{4}\pi (3^2)(2)-\left[5^2-\dfrac{1}{4}\pi (5^2)\right]=16 \pi-\dfrac{9}{2}\pi-\left(25-\dfrac{25}{4}\pi\right)=\dfrac{23}{2}\pi-25+\dfrac{25}{4}\pi=\dfrac{71}{4}\pi-25$

Finally,

$a+b+c=71+4+25=$ $\boxed{100}$

area of the shaded region

The answer is 100.

1 solution

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