Areas of Plane Figures 2

Mathematics J.S.S 3 Third Term

Theme: Measurement and geometry

Sub Theme: Shapes

WEEK 2

Areas of Plane Figures 2

Performance Objectives

Students should be able to;

1. Solve word problems
2. Solve quantitative aptitude problems on areas

Word problems involving area

Content

Example 1

An arc of a circle with a radius of 14cm subtends an angle of 135⁰ at the centre. Calculate the length of the arc. Take π=227.

Solution

Use the formula

l= Ɵ3600 x 2πr 

Where Ɵ = 135⁰

r = 14cm, π = 227

l= 13503600 x 2 x 227 x 14cm 

 L = 0.375 x 88cm

L = 33cm

 

Example 2

The angle subtended by a sector of a circle is 70⁰. If the perimeter of the sector is 105cm, calculate the radius

Solution

Perimeter of a sector = 2r + L

Perimeter = 105cm

Radius r is unknown,

 

l= Ɵ3600 x 2πr 

Therefore l= 203600 x 2 x 227 x r 

l = 11r9 

  Therefore perimeter of the sector = 2r+119r

105 = r 2+119=299r

r = 105 x 929= 94529

= 32.6cm

 

Example 3

Calculate the perimeter of a segment which subtends an angle 90⁰ at the centre of radius 3.5cm.

Solution

Perimeter of a segment = a3600 x 2πr+2rsinaz

a=90, r=3.5 cm

 903600 x 2 x 227 3.5+2 x 3.5 x sin450 

= 11 x 0.5 + 7 x 12

= 10.45cm

 

Example 4

Given that the radius of a circle is 28cm and the length of an arc is 44cm, calculate the angle subtended at the centre. (take π = 22/7)

Solution

Ɵ= ? 

l=44cm,  

 r=28cm 

l= Ɵ3600 x 2πr 

44cm= Ɵ3600 x 2 x 227 x 28 

44cm= Ɵ x 44 x 43600  

 Ɵ= 44 x 3600 44 x 4  

= 90⁰

Example 5

Calculate the perimeter of a sector which subtends an angle of 90⁰ at the centre of a circle with a radius of 21cm.

Solution

Perimeter of a sector = 2r + L

r = 21cm

l= Ɵ3600 x 2πr 

l= 903600 x 2 x 227 x 21cm 

= 33cm

Therefore Perimeter of the sector = 2 x 21cm x 33cm

                                                = 42cm + 33cm

                                                = 75cm