There is a circular pond and a footpath runs along its boundary. A person walks around it, exactly once keeping close to the edge. If his steps is $66 cm$ long and he takes exactly $400$ steps to go around the pond, then find the diameter of the pond?

Area and Perimeter

1. Area of a triangle $=\frac{1}{2}\times \mathrm{Base}\times \mathrm{Height}$

2. Area of a triangle $=\sqrt{\mathrm{s}\left(\mathrm{s}-\mathrm{a}\right)\left(\mathrm{s}-\mathrm{b}\right)\left(\mathrm{s}-\mathrm{c}\right)}$ where $\mathrm{s}=\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{2}$

3. Area of an equilateral triangle $=\frac{\sqrt{3}}{4}\times {\left(\mathrm{side}\right)}^2$

4. Area of a circle $={\mathrm{\pi r}}^2$

5. Circumference of a circle $=2\mathrm{\pi r}$

6. Area of a sector of a circle $=\frac{\mathrm{\theta }}{{360}^{\mathrm{o}}}\times {\mathrm{\pi r}}^2$

7. Area of a square $={\mathrm{side}}^2$

8. Perimeter of a square $=4\times \mathrm{side}$

9. Perimeter of a Rectangle $=2\times \left(\mathrm{length}+\mathrm{breadth}\right)$

10. Area of a Rectangle $=\left(\mathrm{length}\times \mathrm{breadth}\right)$

11. A rhombus is a parallelogram that has all the sides equal. In a rhombus, diagonals always bisect each other. Area $=\frac{1}{2}\times {\mathrm{d}}_1\times {\mathrm{d}}_2$

12. A quadrilateral whose opposite sides are parallel is called a parallelogram. Diagonals of a parallelogram bisect each other. Area $=\mathrm{Base}\times \mathrm{Height}$

13. A trapezium is a quadrilateral with only two sides parallel to each other. Area $=\frac{1}{2}\times \mathrm{Sum} \mathrm{of} \mathrm{parallel} \mathrm{sides}\times \mathrm{Height}$