How do I convert units of area?

Square the linear conversion factor, because area has two dimensions. Area units convert with the square of the length factor. 1 m=100 cm, so 1 m^2=100^2=10\,000 cm^2. To convert from a larger unit to a smaller one, multiply. From a smaller unit to a larger one, divide.

Area & Perimeter Notes

Cambridge IGCSE Maths: Revision notes

Key facts

Perimeter is the distance around the outside: add every outer side.
Rectangle $A=lw$ ; triangle $A=\tfrac12bh$ ; parallelogram $A=bh$ ; trapezium $A=\tfrac12(a+b)h$ .
The height of a triangle, parallelogram or trapezium is the perpendicular height, not a slanted side.
For a compound shape, split it into simple shapes, find any missing sides, then add the areas.
Area units convert with the square of the length factor: $1\text{ m}^2=10\,000\text{ cm}^2$ .

Perimeter

Perimeter is the total distance around the outside of a shape.

Find the perimeter by adding the lengths of all the outer sides. For a rectangle with length $l$ and width $w$ , $P=2l+2w=2(l+w)$ . For irregular shapes, add every side, working out any missing sides first.

A 7 cm by 4 cm rectangle: perimeter = 7 + 4 + 7 + 4 = 22 cm

A rectangle is 9 cm long and 5 cm wide. What is its perimeter?

Area formulas

Use the formula for the shape, with the perpendicular height.

The area of a rectangle is $lw$ . For a triangle, the height must be perpendicular to the base, not a slanted side. A parallelogram uses base × perpendicular height. In a trapezium, $a$ and $b$ are the two parallel sides and $h$ is the perpendicular distance between them. Learn all four: do not rely on the exam paper.

Triangle $A=\dfrac12\times\text{base}\times\text{height}$
Parallelogram $A=\text{base}\times\text{height}$
Trapezium $A=\dfrac12(a+b)h$

Trapezium with parallel sides 10 cm and 6 cm, perpendicular height 4 cm

Worked example

A trapezium has parallel sides 6 cm and 10 cm and height 4 cm. Find its area.

1
Write the formula: $A=\tfrac12(a+b)h$ .
2
Substitute: $A=\tfrac12(6+10)\times4$ .
3
$A=\tfrac12\times16\times4$ .

A triangle has base 8 cm and perpendicular height 5 cm. What is its area?

Compound shapes

Split the shape into simple parts, find missing lengths, then add areas or outer edges.

A compound shape is made from two or more simple shapes. Split it up, find the area of each part and add. Opposite sides of rectangular parts must match, so use addition or subtraction to find missing sides. For the perimeter, add the outer edges only. Internal dividing lines are not part of it.

An L-shape: only some sides are given

Worked example

Find the missing sides, then the area and perimeter of the L-shape.

1
Horizontal: $?+4=8$ , so $?=4$ cm. Vertical: $3+?=6$ , so $?=3$ cm.
2
Split into a lower $8\times3$ and an upper $4\times3$ rectangle: area $=24+12=36$ cm².
3
Perimeter (outer edges only): $8+3+4+3+4+6=28$ cm.

Which edges count towards the perimeter of a compound shape?

Area units

Square the linear conversion factor, because area has two dimensions.

Area units convert with the square of the length factor. $1\text{ m}=100\text{ cm}$ , so $1\text{ m}^2=100^2=10\,000\text{ cm}^2$ . To convert from a larger unit to a smaller one, multiply. From a smaller unit to a larger one, divide.

1 cm²100 mm²
1 m²10 000 cm²
1 km²1 000 000 m²

Worked example

Convert $3.5\text{ m}^2$ to $\text{cm}^2$ .

1
Metres to centimetres is larger to smaller, so multiply.
2
The area factor is $100^2=10\,000$ .

Convert $2500\text{ mm}^2$ to $\text{cm}^2$ .

Try an exam question

(a) A trapezium has parallel sides of 7 cm and 11 cm and a perpendicular height of 5 cm. Work out its area. (b) Change $2.4\text{ m}^2$ into $\text{cm}^2$ .

[4 marks]

That's the notes covered.

Carry on to the next subtopic.