# Lesson Notes By Weeks and Term - Junior Secondary School 3

Area of Plane Figures

SUBJECT: MATHEMATICS

CLASS:  JSS 3

DATE:

TERM: 2nd TERM

WEEK FIVE AND SIX

TOPIC: Area of Plane Figures

Area of Triangle

B                      B

h                        h

A                 b                  C                  D               A      b          C

Area of âABC   =   ½ base X height   =  ½ bh

B

C            h    a

A            b     D                  C

Sin A   =  h

C                h   =   c sin A

Area of âABC  =   ½ bc   sin A

Example 1:

Find the area of triangle PQR if sides PQ  = 6cm, PR  =  8cm  and QR  = 10cm

Solution

First, we need to show that âPQR is a right angled triangle

PQ2  +  PR2    =  QR2

62  + 82   =  102

36  + 64  = 100

âPQR is a right – angled triangle since 6, 8 and 10 Pythagoras triples

Q

6cm        10cm

P        8cm              R

Area of âPQR   = ½ X  8  X  6    =    24cm2

Example 2:

Calculate the area of triangle PQR correct to 3 significant figures if p = 8.5cm, q = 6.8cm and R = 65.40

Solution

P

r

R     65.40                    Q

P   8.5cm

Area of âPQR      = ½ pq sin  65 . 40

= ½ x 8.5 x 6.8 x sin 65.4

=  26.276cm2

Area = 26.3cm2  to 3 s.f

Area of Parallelograms

h

b

Area of parallelogram  = base  x  height  =  bh

Consider the parallelogram

D                          C

A          E                  D

In general,

Area of parallelogram  = product of adjacent sides x the size of angle between the two sides

Example 3

Find the area of parallelogram with base 12cm and height 7cm

Solution

Area of parallelogram  = base x height

=  12cm  x 7cm

=  84cm2

Example 4:

Find the area of parallelogram shown in the diagram below

D                C

550

A         12.5cm               B

Area of ABC â     = 12.5 x 8.4 x sin 55

= 105 x 0.8192

= 86.061cm2

The area of ABC â  = 86.061cmto 1 d.p

Trapezium

A                  a                B

H

D               b             C

Area of trapezium    =   ½ of (sum of parallel sides) x height

Area of trapezium   = ½ (a + b)h

Rhombus

Area of Rhombus   = base  x height

=  bh

OR Area of Rhombus    =  ½  of product of diagonals

Example 3:

Find the area of trapezium  ABCD shown below if AB  = 8cm, BC = 6cm,  DC  = 12cm  and angle BCD  = 430

A        8cm        B

430

D            12cm            C

Solution:

Area of trapezium ABCD   =  ½ (AB + DC)h

Sin 430      = h/6

h   =   6 x sin 430

=  6 x 0.6821  =  4.092

Area of ABCD  =  ½  (8 + 12) x   4.092

= ½ x 20 x 4.0920    = 40.92cm2

The area of trapezium ABCD = 41cm2 to the nearest cm2.

Area of Circles

Area of circle

where    r   =  d/2

Area of annulus

R                     Outer Circle

r            Inner Circle

Annulus

Area of annulus     =   R2  -

=    (R2 – r2)

Essential Mathematics page 220

Ex 21.5 ; 1 – 23

WEEKEND ASSIGNMENT

1. The area of a parallelogram is given as 108cm2. F he height of the parallelogram is 9cm, find the base of the parallelogram    A. 13cm  B. 9cm    C.  12cm
2. Find the area of a rhombus of side 20mm and height 10kk A. 20mm2   B. 200mm2   c.  300mm2
3. Find the area of a circle of diameter 35cm
4. The area of a circle is 1386cm2. Find the diameter of the circle    A. 21CM  B. 42cm  C. 82cm
5. A sector of a circle of radius 8cm has an area of 1200 at the centre. Find its perimeter  A.  33  B.  34  C. 36

THEORY

1. A circle has an area of 144 . Calculate the circumference of the circle, leaving your answer in terms of
2. Calculate the area of an annulus, which has an external diameter of 25cm and internal diameter of 15cm.