Question

The pictures below show circles through the vertices of a square and a rectangle

Calculate the areas of the circles

Answer 1

i. One side of a square is 3 cm, therefore its diagonal is 3√2 cm Diameter of the circle = 3√2 cm

ii. Rectangle inside the circle having length 4 cm and breadth 2 cm.

Diagonal = \(\sqrt{4^2+2^2}=\sqrt{16+4}\)

\(=\sqrt{20}\) cm

Diameter of the circle = √20 cm

Radius = \(\frac{\sqrt{20}}{2}\)cm

Area = \(\pi\times(\frac{\sqrt{20}}{2})^2=\pi\times\frac{20}{4}\)

= 5 π cm²