Area of a Circle

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Area of a Circle: meaning, method and solved example (7th Grade) – Maths PDF

In short: The area of a circle counts the flat space inside its rim, and you get it by squaring the radius and then multiplying by pi, which is the formula A = πr².

7th GradeGeometry7.G.B.4

What is Area of a Circle?

The area of a circle tallies the square units of surface inside the boundary, like the grass a sprinkler waters or the top of a round pizza.

Its formula is \(A = \pi r^2\). Squaring the radius builds a square on that radius, and the circle covers just over three such squares, exactly \(\pi\) of them. Since the radius is squared, doubling it makes the surface four times bigger. Always start from the radius, never the diameter.

How to spot it

  • You need the area of a circle: how much grass, paint, fabric or water surface a round region takes up.
  • A radius or diameter is given and the target is the space inside, in square units.
  • The wording mentions a round rug, circular pond, pizza size or sprinkler range.
  • The final answer must be left in terms of pi, such as 144π square feet.

The method

  1. Get the radius; if the width was given, halve it first.
  2. Square the radius by multiplying it by itself.
  3. Multiply by \(\pi\), keeping the symbol for an exact answer or using 3.14159 for a decimal.
  4. Finish with square units, such as square feet.
r = 12 ftr × r = 144The circle holdsπ ≈ 3.14 such squares.A = π × 144≈ 452.39 sq ft
A square built on the radius has area 144; the circle covers pi of them.

Area of a Circle: solved example

Problem

A round pond in a Minnesota park reaches 12 feet from its center to the shore. How many square feet of water does it cover?

Solution

Square the radius: \(12^2 = 144\).

Multiply by pi: \(A = 144\pi \approx 452.39\). The pond covers 144π ≈ 452.39 square feet.

Try it

Question 1

A round rug is 10 feet across. Give its area in terms of \(\pi\) and then to the nearest hundredth.

Show the answer

\(r = 5\), so \(A = 25\pi \approx 78.54\) square feet.

Question 2

Some circular glass covers \(49\pi\) square centimeters. What is its radius?

Show the answer

\(r^2 = 49\), so \(r = 7\) centimeters.

Area of a Circle vs. Circumference

The area of a circle measures the surface inside, uses \(\pi r^2\) and comes in square units. The circumference measures the edge, uses \(2\pi r\) and comes in plain units. A frequent slip is squaring the diameter, or skipping the halving step, which makes the answer four times too large.

Circumference

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