Area (Edexcel IGCSE Maths)

Area Formulas

Spec point — 4.8E

What is area?

• Area is the amount of space within the perimeter of a 2D shape

  • For example, the size of a sports field

• Area is calculated using lengths in two dimensions

  • Units of measure include mm², cm², m² etc

How do I find the area of a shape on a square grid?

• Count the total number of whole squares inside the shape

  • You can shade or mark the squares you have counted so far

• Parts of the shape may not contain whole squares

  • Pair up half squares, or parts of squares, to form whole ones

• There will be a scale telling you how much area one square represents

  • Multiply the number of squares you have counted by this value to find the total area of the shape

Which area formulas do I need to know?

Formulas for the areas of common shapes

How do I find the area of a rectangle?

• The area, A, of a rectangle of length, l, and width, w, using the formula

  • $A=l\times w$

    • Multiply together the length and the width

How do I find the area of a triangle?

• The area, A, of a triangle with base, b, and length, l, can be found using the formula

  • $A=\frac{1}{2}bh$

    • Multiply the length of the base (b) by the perpendicular height(h)
    • Halve the answer

• The perpendicular height may not be the length of one of the sides of the triangle

How do I find the area of a trapezium?

• The area, A, of a trapezium with parallel lengths, a and b, and perpendicular height, h, can be found using the formula

  • A=1 half (a+b) h

    • Add together the lengths of the parallel sides
    • Multiply the result by the distance between the parallel sides
    • Halve the answer

• You are given this formula in the exam

How do I find the area of a parallelogram?

• You can find the area, A, of a parallelogram of length, l, and perpendicular height, h, by using the formula

  • $A=bh$

    • Multiply the length of the base by the perpendicular height

• The perpendicular height is not a length of the parallelogram

• It is the distance between the base and its opposite side

• You can work the area of a parallelogram out by splitting the shape into a rectangle and triangles if you can't remember the formula

Exam Hint

• You may have to do some work to find missing lengths first

  • For example, you may need to use Pythagoras' Theorem to find a missing length on a triangle

• The area of a trapezium is given to you in the exam but you will need to remember the other formulas

Worked Example Calculate the area of the following shapes.

(a)

Answer:

Find the area of the trapezium using A=1 half (a+b) h Remember that a and b are the two parallel sides and h is the perpendicular height

A=1 half (30+15)×20

Final answer: 450 cm²

(b)

Answer:

Find the area of the parallelogram using $A=b\times h$ Remember that b is the base and h is the perpendicular height

$A=15\times12$

Final answer: 180 cm²

(c)

Answer:

Find the area of the right-angled triangle using $A=\frac{1}{2}bh$ Remember that b is the base and h is the perpendicular height

$A=\frac{1}{2}\times8\times7$

Final answer: 28 cm²