# Area and Perimeter of a Circle

We will discuss the Area and Perimeter of a Circle.

The area (A) of a circle (or circular region) is given by

A = πr2

where r is the radius and, by definition, π = $$\frac{\textrm{Circumference}}{Diameter}$$ = $$\frac{22}{7}$$ (Approximately).

The circumference (P) of a circle, or the perimeter of a circle region, with radius r is given by

P = 2πr

Solved Examples on Area and Perimeter of a Circle:

1. The radius of a circular region is 7 m. Find its perimeter and area. (Use π = $$\frac{22}{7}$$)

Solution:

Here r = 7 m. Then,

Perimeter = 2πr = 2 × $$\frac{22}{7}$$ × 7 m = 44 m;

Area = πr2 = $$\frac{22}{7}$$ × 72 m2 = 154 m2.

2. The perimeter of a circular plate is 132 cm. Find its area. (Use π = $$\frac{22}{7}$$)

Solution:

Let the radius of the plate be r. Then,

Perimeter = 2πr

⟹ 132 cm = 2 × $$\frac{22}{7}$$ × r

⟹ 132 cm = $$\frac{44}{7}$$ × r

⟹ $$\frac{44}{7}$$ × r = 132 cm

⟹ r = 132 × $$\frac{7}{44}$$

⟹ r = $$\frac{924}{44}$$

⟹ r = 21 cm.

Therefore, area of the plate = πr2 = $$\frac{22}{7}$$ × 212 cm2

= $$\frac{22}{7}$$ × 441 cm2

= $$\frac{9702}{7}$$ cm2

= 1386 cm2

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