# Area Of Plane Figures

Welcome to Class !!

In today’s Mathematics class, We will be talking about Area of Plane Figures. We hope you enjoy the class!

##### Area of Plane Figures

Area of Triangle

Example 1:

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

Solution

First, we need to show that ∆PQR is a right angled triangle

PQ2  +  PR2    =  QR2

62  + 82   =  102

36  + 64  = 100

Area of ∆PQR   =

= 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

#### Parallelogram

Area of parallelogram  = base  x  height  =  bh

Consider the parallelogram

In general,

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

Example 3

Find the area of a 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

#### Rhombus

Area of Rhombus   = base x height =  bh

OR Area of Rhombus    =

$\frac{1}{2}$

of the product of diagonals

#### Trapezium

Area of Trapezium =

Example 3:

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

Solution:

Area of trapezium ABCD   =

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

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.

We have come to the end of this class. We do hope you enjoyed the class?

Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.

In our next class, we will be talking about Trigonometry. We are very much eager to meet you there.