How to Find the Area of a Quadrant (a Quarter of a Circle)

A quadrant is a quarter of a circle. So to work out the area of a quadrant, first work out the area of the whole circle (use the formula A = π ×r²) and then divide the answer by 4. Alternatively, you could substitute the radius of the quadrant directly into the formula A = ¼ πr². Let’s take a look at a few examples on working out the area of quadrants:

Example 1

Work out the area of this quadrant (radius 8cm).

Method 1 (using the area of a whole circle and dividing by 4)

First work out the area of the whole circle by substituting the radius of 8cm into the formula for the area of the circle:

A = π ×r²

= π ×8²

= 64π (leave the answer as an exact solution as this need to be divided by 4).

So all you need to do now is divide the answer by 4:

Area of a quadrant = 64π ÷4 = 16π = 50.3 cm² to 3 significant figures.

Method 2 (using ¼ πr²)

Substitute r = 8 directly into the formula A = ¼ πr².

A = ¼ πr².

A = ¼ × π × 8².

A = 50.3 cm²

As you can see it gives exactly the same answer as method 1.

Example 2

Work out the area of this quadrant (radius 3.8m).

Like example 1, begin by substituting the radius of 3.8m into the formula for the area of the circle:

A = π ×r²

= π ×3.8²

= 14.44π (leave the answer as an exact solution as this need to be divided by 4).

Again, all you need to do now is divide the answer by 4:

Area of a quadrant = 14.44π ÷4 = 16π = 11.3 m² to 3 significant figures.

Method 2

Substitute r = 3.8m directly into the formula A = ¼ πr².

A = ¼ πr².

A = ¼ × π × 3.8².

A = 11.3 m²

As you can see it gives exactly the same answer as method 1.