Finding the Area of 2D Shapes

Area of 2D Shapes

It’s not just necessary in the classroom. Finding the area of 2D shapes is an important skill that proves incredibly handy in life.

Whether you’re sizing up a rectangular floor space to see if there’s enough space for your Xbox or choosing the right carpet lengths for your new living room, knowing how to make the correct calculations can go a long way.

However, these skills are also very necessary for exams! And that’s what we focus on here…

Area of 2D Shapes – What’s Covered

This post explains how to find the area of all the 2D shapes you need to know for GCSE. You aren’t given the formula for any of these shapes so you do need to remember them – consider sticking them up somewhere you will look at them regularly or writing revision cards for them.

We will cover:

Area of a Rectangle

To find the area of a rectangle, we simply multiply the width by the length.

Area of 2D shapes - finding the area of a rectangle

Area = 7 Γ— 1.2
          = 8.4cm2

Area of a Triangle

To find the area of a triangle, we multiply the base by the perpendicular height then divide by 2.

Area = (4 Γ— 11) Γ· 2
          = 44 Γ· 2
          = 22cm2

Area of a Parallelogram

A parallelogram is a little trickier than the other shapes. We need to multiply the base by the perpendicular height.

This is the measurement that is at a right-angle to the base of the parallelogram. In this case, 4cm.

Calculating the area of a parallelogram

Area = 4 Γ— 12 
          = 48cm2

Area of a Trapezium

A trapezium is a shape with one set of parallel sides. There are a few ways to find its area but the most reliable method is to use the formula.

The formula labels the parallel sides as \boldsymbol{a} and \boldsymbol{b} and the perpendicular height as \boldsymbol{h}

Then, the area is:
                                      \LARGE\boldsymbol{\frac{1}{2} \times (a + b) \times h}

Area of 2D shapes - area of a trapezium

Area = \boldsymbol{\frac{1}{2} \times (6 + 10) \times 4}
          = \boldsymbol{\frac{1}{2} \times 16 \times 4}
          = \boldsymbol{32} cm2

Some people use this song to remember the formula – it fits to the tune Pop Goes the Weasel.

🎢 Half the sum of the parallel sides,
Times by the difference between them,
That’s the way to calculate,
The area of a trapezium.🎢

Area of a Circle

To find the area of a circle, we need to know the length of the radius. This is the distance from the centre to edge. The area is then Ο€ times the radius squared, or A = Ο€r2.  

Calculating the area of a circle

Area = Ο€ Γ— 102
          = 314.2cm2 (to 1d.p.)

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