The radius of the circumcircle of a right-angled triangle is $3 \mathrm{cm}$ and the perpendicular distance of its hypotenuse from the opposite vertex is $2 \mathrm{cm}$. Find the area of the triangle.

If a square is inscribed in a circle, find the ratio of the areas of the circle and the square.

Prove that the area of the circumcircle of a square is double of the area of its incircle.

Each of the sides of an equilateral triangle is $8 \mathrm{cm}$. Find the radius of the circumcircle and its area.

If the area of the incircle of an equilateral triangle be $48\pi \mathrm{sq}-\mathrm{cm}$, then find the perimeter $\left(\mathrm{in} \mathrm{cm}\right)$ of the triangle.

Find the difference of the areas of the circumcircle and the incircle of an equilateral triangle of sides $6 \mathrm{cm}$.

The area of an equilateral triangle is $100\sqrt{3} {\mathrm{cm}}^2$. Taking each of its vertices as a centre and half of the sides as the radius, three circles are drawn in figure below. Find the area of the region of the triangle which is not closed by the circles. (Take $\sqrt{3}=1.732$, $\pi =\frac{22}{7}$ and round of answer up to $2$ decimal places)

The length of each side of a square park is $100 \mathrm{m}$. There are flower-gardens at each corner of the square. The gardens are the part of a circular region of radius $14 \mathrm{m}$ each (as shown in the figure). Find the area $\left(\mathrm{in} {\mathrm{m}}^2\right)$ of the rest part of the park.