Question

How is the area of a rectangle or a triangle connected to a circle?

Answer 1

Step 1: Area of rectangle and triangle

A diagonal of a rectangle separates the rectangle into two congruent triangles. The area of each triangle is one-half the area of the rectangle.

Area $A_r$ of rectangle is given by

$A_r=bh$

So, the area $A_t$ of a triangle is given by the formula

$A_t=\frac{1}{2}bh$

where $b$ is the base and $h$ is the height of the triangle.

Step 2: Area of a circle

Let, base of the triangle be equal to the circumference of the circle,

$b=2\mathrm{\pi r}$

Let radius of the circle be the height of the triangle,

$h=r$

Therefore, area of a triangle,

$A_t=\frac{1}{2}bh$

$=\frac{1}{2}\times 2\mathrm{\pi r}\times \mathrm{r}$

$={\mathrm{\pi r}}^2$

$=$area of a circle

Hence, the connection between the area of a rectangle or a triangle to a circle has been shown.