Study Guides/Maths/Area of a Quadrant Formula
Study Guide · Maths

How to Find the Area of a Quadrant of a Circle

In geometry, a circle can be divided into four equal parts. Each of these four equal parts is called a quadrant. The central angle of a quadrant is exactly 90 degrees (a right angle). Calculating its area is very straightforward.

Question (Click to Flip)

If the radius of a circle is 7 cm, what is the area of its quadrant?

Answer

Area = 1/4 × (22/7) × (7)² = 1/4 × 22 × 7 = 154 / 4 = 38.5 cm².

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Key Facts

A quadrant is a 90-degree sector of a circle.

The perimeter (circumference curve) of a quadrant is $\frac{\pi r}{2}$.

The total perimeter of a quadrant piece (including the two straight radii) is $\frac{\pi r}{2} + 2r$.

1. The Formula

Since a quadrant is exactly one-fourth (1/4) of a full circle, its area is simply the area of the circle divided by 4.

  • Area of a Quadrant = $\frac{1}{4} \pi r^2$

Where 'r' is the radius of the circle, and $\pi$ (pi) is approximately 22/7 or 3.14.

2. Deriving it from the Sector Formula

A quadrant is just a sector of a circle with a central angle ($\theta$) of $90^{\circ}$. The general formula for the area of a sector is:

  • Area = $\frac{\theta}{360} \times \pi r^2$
  • Substitute $\theta = 90$:
  • Area = $\frac{90}{360} \times \pi r^2 = \frac{1}{4} \pi r^2$.

Questions and Answers

If the radius of a circle is 7 cm, what is the area of its quadrant?+

Area = 1/4 × (22/7) × (7)² = 1/4 × 22 × 7 = 154 / 4 = 38.5 cm².

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