Area Of Plane Figures


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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



Sin A = hch = c × Sin AArea of ABC = 12 bc Sin A


Example 1:

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


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

PQ2  +  PR2    =  QR2

62  + 82   =  102

36  + 64  = 100



Area of ∆PQR   = 

12 × 8 × 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




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


Area of parallelogram = base x height

=  12cm  x 7cm

=  84cm2


Example 4:

Find the area of parallelogram shown in the diagram below





Area of Rhombus   = base x height =  bh

OR Area of Rhombus    = 


  of the product of diagonals




Area of Trapezium = 

12(Base + Top) Height = 12AB + DCh

Example 3:

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



Area of trapezium ABCD   = 

12 × AB + DCh

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



  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



  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.


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