Basic Mathematics Form One Notes – Perimeters and Areas
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Perimeters of Triangles and Quadrilaterals
The Perimeters of Triangles and Quadrilaterals
Find the perimeters of triangles and quadrilaterals
Perimeter — is defined asthe total length of a closed shape. Iti obtained by adding the lengths of
the sides inclosing the shape. Perimeter can be measured in m, cm ,dm ,m,kme.t.¢
Examples
() —_Arectangle of length J and width w
L
[L__|*
Perimeter, P = 1+ 1+ w +w = 21+ 2w =2(I+w)
P=20+w)
(ii) Asquare of side !
O
Perimeter,P =1+1+1+1=4l
Example 1
Find the perimeters ofthe following shapes
() 7m ® o gem
4m ne |
129
Solution
a. Perimeter = 7m + 7m +3m-+3m=20m
b. Perimeter =2m + 4m +5m=11 m
c. Perimeter = 3m + 6em-+ dem + Sem+5 em+4em=27 em
Circumference of a Circle
The Value of Pi (II)
Estimate the value of Pi (11)
commonly approximated 3.14159. It has been represented by the Greek letter “x” since the mid
18th century, though itis also sometimes spelled out as “pi” /pav).
Experiments show that the ratio ofthe circumference to the diameter is the same forall circles
circumference
ie —— = constant number called,
diameter
c
San
d
Where c = circumference of acircle, d = diameter of the circle
But d=2r,then
Where r= radius of the circle
The Circumference of a Circle
330
Calculate the circumference of a circle
Example 2
Find the circumferences of the celes with the following measurements. Take m= 3.14
a. diameter 9.em
b. radius 34m
©. diameter 4.5 dm
d radius 8 km
Solution
(a) C= md = 3.14 x 9 = 28.26 cm
(o) C= 2ar=2 x 3.14 x 35= 6.28 x 2=2198m
() C= nd = 3.14 x 45 = 14.13 dm
(4) C= 2nr =2 x 3.14 x 8 = 50.24 km
Example 3
The circumference of a car wheel is 150 cm. What isthe radius of the wheel?
Solution
Given circumference, C= 150 em
C= 2ar
C __150__ 150 5,
“292×314 628° TM
+: The radius ofthe whee is 23.89 em
Areas of Rectangles and Triangles
The Area of a Rectangle
Calculate the area of a rectangle
131
‘Area ~ can be defined as the total surface covered by a shape. The shape can be rectangle,
square, trapezium e. t. c. Area is measured in mm!, em!,dm!,m! e. t.¢
Consider a rectangle of length | and width w
U
Li”
Area, A=l x w=lw
Consider a square of side 1
O
Area,A=Ixl
Consider a triangle with a height, h and a base, b
b
Ai A Ly
rea, A =>
Areas of Trapezium and Parallelogram
The Area of a Parallelogram
132
Calculate area of a parallelogram
‘A parallelogram consists of two triangles inside. Consider the figure below
b
‘Area, A = bh
The Area of a Trapezium
Calculate the area of a trapezium
Consider a trapezium of height, h and parallel sides a and b
a
D
T
Area,A = >h(a +b)
Example 4
The area of a trapezium is120 m!. Its height is 10 m and one of the parallel sides is 4 m. What is
the other parallel side?
Solution
Given area, A= 120m, height, A= 10 m, one parallel side, a = 4 m. Let other parallel side be, b
Then
133
1
A=zh(a+b)
1
120 = 5 x 10x (4+)
120 =5x(4+b)
4+b= 120
“5
44b=24
b=24-4=20
+ The length of other parallel side is 20 m
Area of a Circle
Areas of Circle
Calculate areas of circle
Consider a circle of radius r;
134
Also r=, then
oa 2 () nd?
rea, A= nr? =n (5) = “7
rea, A =~
Example 5
Find the areas of the following figures
Co) Sm 1) rc) 6mm
TS em, tm
@ “x ©
m
Solution
135
(a) A=lw=5x 3=15m?
(b) A = bh = 7.5 x 15 = 11.25em?
() A= Zh(a+b) =F x4x (648) =F x4x 14 = 28 mm?
(d) A=5hb=3 x 2x 6=6m?
(e) A=ar? -2 x 12? -2 x 144 = 888 = 452.57 cm?
Example 6
A circle has a circumference of 30 m. What is its area?
Solution
Given circumference, C = 30 m
C=2ar
£30 0,
“” oe” Txat 62647″
Then
12 12 5027 :
Ann? =% 5 470) = 2 x 2285 = = 191 m
136