Areas, Shapes and Perimeters

How to recognise, measure and calculate

Common Shapes

• There are many types of shape including pentagons, dodecahedrons, rhomboids and trapeziums.

• All straight edged shapes can be split into triangles.• Compound shapes are irregular shapes made up of similar

shapes. By breaking these down into their component parts we can work out their dimensions.

• Being able to recognise a few basic shapes we can more readily break down more complex shapes into their component parts and so measure and calculate the correct dimensions.

Triangles

• Triangles are easily recognisable due to their three straight sides.• The internal angles of a triangle add up to a total of 180o.• Where all the sides of a triangle are of equal length the triangle is

know as an equilateral triangle.• Where any two of the sides are of equal length the triangle is known

as an isosceles triangle.

Squares

• The internal angles of a square add up to 360o, 90o at each corner.

• All the sides of a square are of equal length.

• A square can be split into two right angled, isosceles triangles.

• We use the total of number of one by one squares any shape would cover to define the area.

Circles

• Circles are shapes with no straight edges.• Any point on the curve of the circle is the same distance from its centre

as any other point on the curve.• Working out the dimensions of circles or segments involves using a

constant known as Pi (Π) and has an approximate value of 3.14.• Often when working with circles and segments people use radians to

measure the angles.

π x diameter = circumference

π x (radius)2 = area

Rectangles

• A rectangle is a four sided shape where the internal angle of each corner is 90o.

• The opposite sides of a rectangle are equal in length.• A rectangle may be split into two right angled triangles.• Rectangles are one of the most common types of shape and most

compound shapes can be split into rectangles of various sizes to easily calculate the dimensions.

Parallelograms

• A parallelogram is a four sided shape where the opposite sides run parallel to each other.

• The opposite sides of a parallelogram are of equal length.• If all the sides of a parallelogram are equal in length it is know as a

rhombus.• You can calculate the area of a parallelogram by cutting the end off

and using it to make a rectangle.

Trapezium

• A trapezium has two parallel sides.• By taking the average length of the parallel sides you can calculate

the area as though it were a rectangle.• A trapezium can be split into two right angled triangles and a

rectangle.• In the US the shape is referred to as a trapezoid.

Perimeter

• The perimeter is the length of the outside edge of any shape.

• For any shape by adding together the total length of all the shapes sides you will establish the perimeter.

• The perimeter of a circle is equal to the length of its only side also known as its circumference.

• The perimeter might also be referred to as the edge.

• When working out the size of a boundary you are calculating the perimeter.

Area

• The area of a shape is worked out by calculating the total number of 1 by 1 squares it covers.

• Partially covered squares are included in equal proportion to the amount of the square covered.

• Because of the method of calculating areas, multiplying two lengths together, the units they are measured in are squared units (e.g. metres [m] become metres squared [m2]).

• Area is used frequently in a large variety of roles, from landscaping to decorating, from construction to printing.

Examples

• Find the area and perimeter of the following shape.

4 m

4 m

Examples

• Find the area and perimeter of the following shape.

4 m

4 m

Area = 16 m2

Perimeter = 16 m

Examples

• Find the area and perimeter of the following shape.

3 m

6 m

Examples

• Find the area and perimeter of the following shape.

3 m

6 m

Area = 18 m2

Perimeter = 18 m

Examples

• Find the area and perimeter of the following shape.

2 m

2 m

4 m

4 m

Examples

• Find the area and perimeter of the following shape.

2 m

2 m

Area = 12 m2

Perimeter = 16 m

4 m

4 m

Basic Rules

• Perimeter = total length of all the sides added together.• Areas

– Square = Length of any side squared. (a2)– Rectangle = Length of one side times the length of an adjacent side. (a x b)– Triangle = Length of the base times the height all divided by 2. ((b x h) / 2)– Parallelogram = Length of the base times the height. (b x h)– Trapezium = Length of the parallel sides totalled together and divided by 2 with

the result multiplied by the height. (((a + b) / 2) x h)

• Circles– Perimeter = Circumference = π x Diameter– Area = π x Radius2

Questions• Calculate the Perimeter and Area of the following quadrilaterals:

5m6m

8m

8m

3m

6m

2m

6m

4m

12m

3m6m

Questions• Calculate the Perimeter and Area of the following quadrilaterals:

5m6m

8m

8m

3m

6m

2m

6m

4m

12m

3m

16m

24m

32m

18m

32m

16m36m2 6m

18m2

12m2

48m2

15m2

64m2

Questions• Work out the Perimeter and Area of the following triangles:

5m

3m

4m

6m

7m

6m

4m

6m

8m4m

5m 5m5m 3m

Questions• Work out the Perimeter and Area of the following triangles:

5m

3m

4m

6m

7m

6m

4m

6m

8m4m

5m 5m5m 3m 18m

6m2

16m

10m2

17m

12m212m

12m2

Questions• Work out the Perimeter and Area of the following compound shapes:

7m

9m

5m

3m

4m3m

2m

2m

2m

2m

2m2m

Questions• Work out the Perimeter and Area of the following compound shapes:

7m

9m

5m

3m

4m3m

2m

2m

2m

2m

2m2m

36m

45m2

24m

20m2

Questions• Calculate the Perimeter and Area of the following shapes:

7m2m

7m

2m

4m

4m

4m

4m

5m

4m4m

3m

6m

Assumeπ = 3.14

Questions• Calculate the Perimeter and Area of the following shapes:

7m2m

7m

2m

4m

4m

4m

4m

5m

4m4m

3m

6m

25.12m

50.24m2

18m

12m2

14m

9m2

20m

22m2

Assumeπ = 3.14