CLASS: JSS 1
TERM: 3rd TERM
TOPIC: PERIMETER OF REGULAR PLANE SHAPES
The perimeter of a plane shape is the length of its outside boundary or the distance around its edges.
An irregular shape does not have a definite shape. To determine the perimeter of such shape, string or thread can be used to measure it. Place the string around the edge, then straighten it out and measure it with a ruler from the mark part.
A regular shape has a well-defined edge which may be straight lines or smooth curves. Examples are regular polygon and circles
The unit of measurement
Perimeter is measured in length units. These are kilometres (km), metres (m), centimetres (cm) and millimetres (mm).
Use a ruler to measure the perimeter of triangle ABC.
By measurement: AB: AB = 21mm, BC = 30mm, AC = 14mm
Perimeter =Total length of sides
= AB + BC +AC
=21mm+ 30mm +14mm
Using formulae to calculate perimeter
The longer side of a rectangle is called the length and is usually represented by letter l. The shorter side is called the width or breadth and it may be represented by w ( or b).
A lcm B
AB = DC = lcm and AD = BC = bcm
Perimeter (P) = AB + BC + CD + DA = l + b + l + b
= 2l + 2b = 2(l + b)
P = 2 ( l + b)
Note: This is also used to determine the perimeter of a parallelogram
The length of a rectangular room is 10m and the width is 6cm. Find the perimeter of the room.
Length of the room, l = 10m ; width/breadth of the room, w (or b) = 6m
Perimeter = 2(l +b) = 2 (10m + 6m)
= 2 ( 16m) = 32m
Calculate the perimeter of a square whose length is 8cm.
A square has all its four sides equal, so each length is l cm.
The perimeter = l +l + l + l = 4l
= 4 8 = 32m
In general, perimeter of a square, P = 4l. This is also used to determine the perimeter of a rhombus
A rectangle has a perimeter of 74m. Find: (a) the length of the rectangle if its breadth is 17m, (b) the breadth of the rectangle if its length is 25m.
Note: since perimeter of a rectangle = 2( l + b)
Length = perimeter of rectangle2- breadth; Breadth = perimeter of rectangle2- length
So, to find the length
(a) Length = perimeter of rectangle2- breadth
= 74m2-17m= 37m – 17m = 20m
(b) breadth= perimeter of rectangle2- length
=74m2- 25m = 37m – 25m = 12m
Perimeter of triangles
The perimeter = a +a +b = 2a +b
Perimeter = a + a + a = 3a
An isosceles triangle has a perimeter of 250mm. If the length of one of the equal sides is 8cm, calculate the length of the unequal side.
First convert to the same unit of measurement
250mm = 25cm
Sum of equal sides = 8cm + 8cm = 16cm
The length of the unequal side = 25cm – 16cm = 9cm
The perimeter = p + q + r + s
The perimeter = a + b + a + c = 2a + b + c
An isosceles trapezium has a perimeter of 50cm if the sizes of the unequal parallel sides are 12cm and 8cm. Calculate the size of one of the equal sides.
Perimeter = 50cm
Perimeter of an isosceles triangle = 2 (equal sides) + b + c = 2x + 8 + 12
50 = 2x + 20
50 -20 = 2x + 20 – 20
2x = 30 ; x = 15cm
Therefore, one of the equal sides = 15cm
Perimeter of Circles
The circumference (C) of a circle is the distance around the circle. This means that the circumference of a circle is the same as its perimeter.
AB = diameter, OA = OB = radii
But AB = OA + OB i.e. d = r + r
diameter , d = 2 radius (r) or radius, r = diameter (d)/ 2
The circumference, C of a circle is given by C =D, where D is the diameter of the circle. If R is the radius of the circle, then C = 2R.
Therefore, C = D or C = 2R
Calculate the perimeter of a circle if its (a) diameter is 14cm (b) radius is 4.9cm (Take π=227).
Perimeter , C = D = 227 × 14 = 44cm
Perimeter = 2R
= 2 227 × 4.9 = 30.8cm
Calculate the perimeter of these figures. (Take π=317).
The perimeter of a circle = D = 317 3.15
= 227 ×3.15 = 9.9cm
The length of the curved edge = 9.9cm2= 4.95cm
The perimeter of the shape = 4.95cm + 3.15 cm = 8.1cm
The perimeter of a circle = 2R = 2 ×317 × 0.63 = 3.96m
The length of the curved edge = 3.96m4 = 0.99m
Perimeter of the shape = 0.99m + 0.63m + 0.63m = 2.25m
AREA OF PLANE SHAPES
The area of a plane shape is a measure of the amount of surface it covers or occupies. Area is measured in square units, e.g. square metre (m2), square millimetres (mm2).
Finding the areas of regular shapes
Area of Rectangles and Squares
A rectangle 5cm long by 3cm wide can be divided into squares of side 1cm as shown below.
By counting, the area of the rectangle is 15cm2. If we multiply the length of the rectangle by its width the answer is also 15cm2 i.e. length X width = 5cm X 3cm = 15cm2
In general, if A = area, l = length and w= width,
Area of a rectangle = length X width
Calculate the area of a rectangle of length 6cm and width 3.5cm.
Area = length X width = 6cm X 3.5cm = 21cm2
The area of a rectangular carpet is 30m2. Find the length of the shorter side in metres if the length of the longer side is 6000mm.
First convert the length i.e. 6000mm to metres
6000mm= 11000 ×6000m = 6m
If A= area, l = length and b = breadth
Using breadth = Arealength ; breadth = 30m26m = 5m
The length of the shorter side is 5m
A square has all its sides equal.
Area = ( length of one side)2 i.e. A = l2
If Area, A is given then the length, l can be found by taking the root of both sides i.e. l = A.
Calculate the area of a square advertising board of length 5m.
Area of square board = l X l = 5m X 5m =25m2
Area of shapes made from rectangles and squares
Calculate the area of the shape below. All measurements are in metres and all angles are right angles.
3 10 2
3 6 4
The shape can be divided into a 3X3 square, 6X10 and 2X4 rectangle.
Area of shape = Area of square + area of 2 rectangles
= ( (3X3) + (6X10) + (2 X4))m2
= 9 + 60 + 8 = 77m2
Area of parallelograms
Area of a parallelogram = base X height
Calculate the area of a parallelogram if its base is 9.2cm and its height is 6cm.
Area of parallelogram = base X height = 9.2cm X 6cm = 55.2cm2
Area of Triangles
In general: Area of any triangle = 12 × base height i.e12× the area of a parallelogram (or rectangle that encloses it).
Calculate the area of the triangle with base 6cm and height 4cm.
Base (b) = 6cm, Height (h) = 4cm
Area = 12 × base height = 12 × 5 4 = 10cm2
Given that the area of triangle XYZ is 120cm2 and its height YD is 12cm. Find the length XZ.
Let the base XZ be bcm; Height, YD (i.e. h)= 12cm
Area of triangle XYZ= 12 × base height
120 = 12 × b 12
b = 20cm
the length XZ is 20cm.
Area of trapezium
Area of trapezium = 12a+bh
Where (a + b) is the sum of the parallel sides and h, the height of trapezium.
Calculate the area of trapezium with the dimensions shown in the figure below.
Area of trapezium = 12sum of parallel sides ×height
=1218+10 ×12 = 12 × 28 ×12 = 168cm2
Area of Circles
Area, A =r2 or A = d24
Find the area of a circle with radius 4.9cm (Take π=227).
Area of a circle = = 227 4.92 cm2
The area of the circle is 75.46cm2 πr2
Find the area of a semicircle with diameter 20mm. (Take = 3.14)
Diameter, d = 20mm; Radius, r = 20/2 = 10mm
Area of a semicircle = 12 ×area of a circle = 12 × πr2
= 12 ×3.14 × 102 = 157mm2
Area of the semicircle = 157mm2
General Evaluation/Revision Questions
Essential Mathematics for J.S.S 1 by A. J. S Oluwasanmi, page 198-209.
(b) 7.6cm (c) 6.9cm (d) 6.4cm
(b) 16cm (c) 24cm (d) 36cm
(b) The area of a parallelogram is 8.5m2 and its base is 500cm. Find its height.
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