Question

In the given Figure. ABC is is a triangle right-angled at $A$ , with $AB=21cm$ and $AC=42cm$ With the vertices $A,B$ and $6$ as centres, arcs are drawn each of radius $10CM.$ Find the area of the shaded region. $(use\pi =3.14)$

Answer 1

The sides of triangle $21cm,42cm$

The area of triangle is $\frac{1}{2}\times 42\times 21=441c{m}^2$

The sectors at corners have same radius $10cm$

So the total area of sectors is combines sector of angle equal to sum of all angles

The Angles in triangle sum up to give $180$

So the total area of sector is $\frac{180}{360}\times \pi {10}^2=50\pi c{m}^2=157c{m}^2$

The area of shaded region is given as $441-157=283c{m}^2$

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