Perimeter is the distance all the way round the edge. Area is the amount of flat space inside. If a field is your shape, the perimeter is how much fencing you need and the area is how much grass there is.
Perimeter is measured in cm, m or km. Area is a length times a length, so it is measured in square units, written with a small two. If your area answer has no small two, you have probably worked out a perimeter by mistake.
Why area is counted in squares
Lay a shape on squared paper and count how many one centimetre squares fit inside. For a rectangle 5 long and 3 wide there are 3 rows of 5, so there are 5 times 3 squares. That single observation is where the formula comes from.
The formulas, and where each comes from
| Shape | Perimeter | Area |
|---|---|---|
| Rectangle | 2(l + b) | l × b |
| Square | 4l | l × l |
| Triangle | Add the three sides | ½ × b × h |
| Parallelogram | 2(a + b) | b × h |
| Trapezium | Add all four sides | ½ × (a + b) × h |
A parallelogram: cut the triangle off one end and slide it to the other, and you have a rectangle with the same base and height. A triangle: a second copy upside down makes a parallelogram, so one triangle is half. Learn these moves and you never have to memorise the formulas.
The height is measured at right angles to the base, never along a sloping side. If a question gives both a slant length and a dashed height, the dashed one is the one the formula wants.
Compound shapes
An L-shaped room has no formula of its own and does not need one. Cut it into two rectangles and add, or take the big rectangle and subtract the missing piece. Both give the same answer, and doing it both ways is the neatest possible check.
When you split a shape to find the area, the cutting line is an inside line and is not part of the perimeter. Walk right round the outside with your pencil and add only the sides you actually travel along.
20 metres of fencing encloses 9 square metres as a 9 by 1, 16 as an 8 by 2, and 25 as a 5 by 5. Same fence, wildly different amounts of grass. The squarer the shape, the more area you get for the same perimeter.
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A rectangular field is 45 m long and 28 m wide. Find the cost of fencing at Rs 120 per metre and turfing at Rs 65 per square metre.
An L-shaped room. The outer rectangle is 8 m by 6 m with a 3 m by 2 m corner missing. Find its area two ways.
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Perimeter is the distance right round the edge. Area is the flat space inside.
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