Area of a rectangle and a square

What is area?

Area is the amount of region enclosed by a closed figure, the space it covers on the page or on the ground. Perimeter tells you how long the edge is; area tells you how much is inside.

We measure area by counting squares. A square with sides of 1 cm has an area of 1 square centimetre (1 sq cm). A square with sides of 1 m has an area of 1 sq m.

Why squares? Squares fit together with no gaps and no overlaps, so they cover a shape completely and can be counted easily. Circles leave gaps, and other shapes are harder to count in neat rows.

Why is the area of a rectangle length × breadth?

Draw a rectangle 6 cm long and 4 cm wide on squared paper. You will see 4 rows, each with 6 squares of 1 sq cm. Instead of counting all of them, multiply: 6 × 4 = 24.

Area of a rectangle = length × breadth

And the area of a square?

A square is a rectangle whose length and breadth are equal, so:

Area of a square = side × side

Example: a square tile with sides of 3 cm covers 3 × 3 = 9 sq cm.

How do you find a missing side?

Divide the area by the side you know.

• A rectangular garden is 20 m long and has an area of 360 sq m. Width = 360 ÷ 20 = 18 m.
• A square has an area of 49 sq cm. Which number times itself is 49? 7 × 7 = 49, so the side is 7 cm.

How do you find the area of shapes made of rectangles?

There are two easy ways.

1. Split it into rectangles, find each area and add them. An L-shaped room made of a 5 m × 3 m part and a 2 m × 2 m part has an area of 15 + 4 = 19 sq m.
2. Take a big rectangle and subtract the part that is missing. A room 6 m × 5 m (30 sq m) with a 4 m × 3 m carpet (12 sq m) has 30 − 12 = 18 sq m of floor without carpet.

How do you estimate the area of an odd shape?

Trace the shape on squared paper where each square is 1 sq unit, then:

• count every full square as 1 sq unit,
• count a square that is more than half covered as 1 sq unit,
• count a square that is exactly half covered as ½ sq unit,
• leave out squares that are less than half covered.

Add them up. The answer is an estimate, close to the real area.

Can the same area have different perimeters?

Yes. Here are the rectangles with whole-number sides and an area of 24 sq units:

Rectangle	Area	Perimeter
1 × 24	24 sq units	50 units
2 × 12	24 sq units	28 units
3 × 8	24 sq units	22 units
4 × 6	24 sq units	20 units

The long, thin rectangle has the greatest perimeter, and the one closest to a square has the least. If you compare perimeters, see perimeter of a rectangle and square.