Area and Perimeter – GCSE Maths

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Introduction

Arrow pointing to the shaded area of a purple rectangle representing the concept of area

  • The amount of space inside of any 2-Dimensional shape is Area.
  • Calculation of area for every shape is done in different way.
  • The Area is measured in square units.

Arrow pointing to the border of a rectangle representing the perimeter

  • The sum of sides of any shape it is made up of is known as Perimeter (the distance around a shape)
  • Calculation of Perimeter for almost every shape is common.
  • The Perimeter is measured in linear units.

Area and Perimeter of Different Shapes

  • Area and Perimeter of Different Shapes:

SQUARE:

Diagram of a square with both sides labeled 'a' to illustrate.

  • Area: a × a = (side)²
  • Perimeter: a + a + a + a = 4a (4 × sides)

RECTANGLE:

Blue rectangle labeled with length L and breadth B.

  • Area: l × b
  • Perimeter: 2 × (l + b)

CIRCLE:

Green circle with radius 'r' marked to demonstrate formulas.

  • Area: π × radius²
  • Perimeter: 2 × π × radius

TRIANGLE:

Pink triangle labeled with base 'b' and height 'h'.

  • Area: (1/2) × base × height
  • Perimeter: sum of all three sides

TRAPEZIUM:

Teal trapezium with sides a, b, c, d and height.

  • Area: (1/2) × (a + b) × h
  • Perimeter: a + b + c + d

Real life Examples of Area and Perimeter

Illustration showing football field, pizza, house, and a thinking child to explain area and perimeter concepts

certified Physics and Maths tutorSolved Example

Problem: Find the area and perimeter of circles with radius equal to:

(i) r = 5cm

(ii) r = 7cm

Two coloured circles with radii labeled 5cm and 7cm to compare area and perimeter

Solution: 

(i) The Area and Perimeter of circle with radius 5cm:

Step-by-step calculation of the area and perimeter of a circle with a radius of 5 cm using π = 3.14

(ii) The Area and Perimeter of circle with radius 7cm:

Step-by-step example calculating the area and perimeter of a circle with a 7 cm radius using π = 3.14

Final Answer: (i) 31.4 cm and (ii) 43.96 cm

certified Physics and Maths tutorSolved Example

Problem: If a rectangular field is of of following dimensions find the its area and length of required fence for the field: Length = 20cm, Breadth = 15cm

Farmers working in a crop field with fences on the side to represent area and perimeter visually

Solution: 

To find the length of required fence for the field we will find out the perimeter:

Worked example of area and perimeter of a rectangle using length 20 cm and breadth 15 cm

Final Answer: Area = 300 cm2 and Perimeter = 70 cm

certified Physics and Maths tutorSolved Example

Problem: Find the Area and Perimeter of the following 2 Dimensional shapes

Labeled diagram showing a trapezium, square, and triangle with side lengths and heights for area and perimeter comparison

Solution: 

(a) The Area and Perimeter of Trapezium:

Worked example showing how to calculate the area of a trapezium using parallel sides 3 cm and 5 cm, and height 5 cm

Perimeter of Trapezium:

Worked example showing perimeter as the sum of 3 cm, 3 cm, 4 cm, and 4 cm to give 14 cm

(b) Area and Perimeter of a square having a side equal to 4cm:

Worked example calculating area and perimeter of a square with side 4 cm

(c) Area and Perimeter of a Triangle with base equal to 4cm and height equal to 4cm:

Worked example showing how to calculate the area and perimeter of a triangle with base and height 4 cm

Final Answer: (a) Area = 36.2 cm2 and Perimeter = 14  cm, (b) Area = 16 cm2 and Perimeter = 16 cm, (c) Area = 8 cm2 and Perimeter = 12 cm

certified Physics and Maths tutorSolved Example

Problem: Work out the area of the following shapes

Diagram of two compound shapes: one with semicircles and a rectangle, another with a notched rectangle; all dimensions labeled

Solution: 

(a) The shape is combination of three shapes the two semi-circles and one square.

The area of this shape will be:

Worked example calculating the area of a compound shape made of two semicircles and a square

(b)The shape is combination of two Rectangles and one square:

Worked example calculating area of a compound shape made from two rectangles and a square

Final Answer: (a) 81.52 cm2 and (b) 33 cm2

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