# Plane Shapes 2: Perimeter – Perimeter of a Rectangle and Square

Perimeter is the outside boundary or edges of a plane shape.

Example

1. Irregular shapes. Measure the perimeter of the quadrilateral ABCD in the diagram below.

Solution

AB = 22mm    = 2.2cm

BC= 27mm      = 2.7cm

CD= 10mm     =1.0cm

DA= 35mm     = 3.5cm

Total 94mm     = 9.4cm

• Regular shapes: Find in cm, the perimeter of the regular hexagon ABCDEF below.

Solution

Length AB= 1.6cm ,

there are 6 equal sides

Perimeter = 6 x 1.6cm

= 9.6cm

Using Formulae to Calculate Perimeters.

Examples

1. A rectangular piece of land measures 57m by 42m. What is the perimeter of the land.

Solution

Perimeter of land     = 2(L + B)

= 2(57 +42) m

= 2(99) m = 198m.

To calculate Length = perimeter of rectangle – breadth

2

To calculate Breadth = perimeter of rectangle/2 – length

• A rectangle has a perimeter of 74m. Find
• a) the length of the rectangle if its breadth is 17.
• b) the breadth of the rectangle if its length  is 25m.

Solution

a) Length = perimeter of rectangle/2 – breadth ,           74m/2  -17m = 37m – 17m = 20m

b) Breadth= perimeter of rectangle/2 – length, 74m/2 – 25m = 37m – 25m = 12m

Squares

A square is a regular four sided shape.

If the length of one side of a square is L.

Perimeter of square = L x 4 = 4L

Length of side of square = perimeter of square/4

Example

1. Calculate the perimeter of a square of side 12.3cm.

Solution

Perimeter of square = 4L, 12.3 x 4 = 49.2cm

• A square assembly area has  a perimeter of 56m. Find the length of the side of the assembly area.

Solution

Length of square = perimeter/ 4  , 56m/4  = 14m

Assignment

1. A rectangular field measure 400m by 550m. What is the perimeter of the field.
2. Calculate the perimeter of a square of side 15cm.
3. A length of wire is bent to make a square of side 3.2cm. a) what is the length of the wire in the square. b)if the wire is silver, costing ₦50 per centimeter, what is the cost of the square.