StopLearnStopLearnPerimeter is the outside boundary or edge of a plane shape. For example, the boundary fence of your school compound is its perimeter. We also use the word perimeter to mean the length of the boundary.
For example, if you take 200 paces to walk your school boundary, you could say its perimeter is 200 paces.
To find the perimeter of a shape, we add together the length of all sides of the shape.
What is the perimeter of the above shape?
Perimeter = 3 + 3 + 2 + 1 + 1 + 2
= 12 cm
Perimeter of a Circle
The perimeter of a circle is called its CIRCUMFERENCE = 2πr
Where r = radius of a circle and
π = 22/7 or 3.14.
Example:
The circumference of a Circle is 44cm. Find its diameter
Solution:
Circumference = 2πr
2πr = 44cm
2 × 22/7 × r = 44
44/7 × r = 44
Divide through by 44/7
r = 44 ÷ 44/7
r = 44 × 7/44
r =7cm
The diameter of a circle = 2 × radius, r.
= 2 × 7cm
= 14 cm.
Solution:
Circumference = 2πr
2πr = 44cm
2 × 22/7 × r = 44
44/7 × r = 44
Divide through by 44/7
r = 44 ÷ 44/7
r = 44 × 7/44
r = 7cm
The diameter of a circle = 2 × radius, r.
= 2 × 7cm
= 14 cm.
Perimeter of a Triangle
Example:
Find the perimeter of these triangles
Solution:
(i) Equilateral triangles have equal sides.
Perimeter = 5cm × 3 sides = 15 cm
(ii) Perimeter of the triangle = 12cm + 5cm + 13cm
= 30 cm
Perimeter of a Regular/Irregular Polygon
The simplest way to find a perimeter of any regular shape is to measure it directly with a ruler. Or tape measure.
Examples:
Length of side AB = 1.6 cm.
There are 6 equal sides, so
Perimeter = 6 × 1.6cm
=9.6 cm
If a shape has a curved side, use a piece of thread to get the shape of the curve. Make the thread straight and measure its length against a ruler.
2. Measure the Perimeter of the shape in the figure below
Straight edges:
AB = 14 mm =1.4 cm
BC =14 mm =1.4 cm
Curved edge:
CA = 22mm approximately
= 2.2 cm
Perimeter (total) = 50 mm approximately
= 5.0 cm
EVALUATION
Use a ruler to measure the perimeters of the shapes. Give your answers in cm.
Perimeter of a Square
A square is a regular four- sided shape. If the length of one side of a square is l, then,
Perimeter of square = l × 4 = 4l
As perimeter of square= 4l,
Length of side of square = perimeter of a square/4
Examples:
Solution:
Perimeter = 12.3cm × 4
Perimeter = 49.2 cm
Solution:
Length = 56/4
= 14 m
Note: The formulae for perimeters of rectangles and squares can be useful. However, if you find it difficult to remember formulae, always sketch the given shape and work from that.
Perimeter of Rectangles
The longer side of a rectangle is called length, and the shorter side is called breadth. We use the letter l and b to stand for the length and the breadth.
Perimeter of rectangle = l + b + l + b
= (l + b) + (l + b)
= 2 × (l + b)
= 2(l + b)
This formula can be used to calculate the perimeter of a rectangle.
Example:
Solution:
Perimeter of field = 2(l+ b)
= 2 × (80 + 50) m
= 2 × 130m
= 260 m.
Solution:
Perimeter of land = 2(l + b)
= 2(57+ 45)m
= 2 × 99m
= 198 m.
Perimeter of a Trapezium
Example:
Find the perimeter of the trapezium below.
Solution:
Perimeter of the rectangular bottom:
= 2(L + B)
= 2(4 + 2)
= 2 × 6
= 12 cm
Perimeter of the triangular top:
Solution:
Let the unknown side be x.
By Pythagoras’s rule;
x² = 3² + 4²
x² = 9 + 16
x² = 25
x = √25cm
x = 5 cm
Perimeter of a Parallelogram
Perimeter of a parallelogram = x + y + x + y = 2 (x + y)
Example:
The perimeter of a parallelogram is 48cm. If one side is 15cm, find the adjacent side.
Solution:
Perimeter = 48cm, x = 15cm, y = adjacent side
Perimeter = 2(x + y)
48 = 2(15 + y).
Divide both sides by 2:
24 = 15 + y
24 – 15 = y
y = 9 cm
Therefore the adjacent side = 9 cm.
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