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Area of a Trapezium 20 m

Mr Arora’s younger brother Bhushan has bought a plot near main
road. But unlike the rectangular plots in Mr Arora’s neighbourhood, 12 m
the plot has only one pair of parallel opposite sides.
Can you identify the shape of the plot? It is nearly a trapezium in 30 m
shape. Can you find out its area?
20 m
Let us name the vertices of this plot as shown in the adjacent figure. By A E
drawing EC || AB, we can divide it into two parts, one in rectangular shape
and the other in right-angled triangular shape, right-angled at C. 12 m h
1 1
So, area of DECD = hc×= × 12 m × 10 m = 60 m 2
2 2 B C D
2
And, area of rectangle ABCE = h × a = 12 m × 20 m = 240 m . 20 m 10 m
a c
\ Area of trapezium ABDE = Area of DECD + Area of rectangle ABCE b
= (60 + 240) m = 300 m .
2
2
We can write the area by combining the two areas and write the area of trapezium as:
Area of ABDE = 1 hc ha×= h  c + a  
×+

2  2 
+ )
++
= h  c + 2 a = h  ca a   = h × (ba = height × (sum of parallel sides )






2
2
2
2
1
1
Hence, the area of a trapezium = × height × (sum of parallel sides) = × h × (a + b)
2 2
By substituting the values of a, b and h in the above expression, we can find the area of the
1 1
trapezium-shaped plot as × h × (a + b) = × 12 × (20 + 30) sq. m = 300 m 2
2 2 b
In the same locality, there is a neighbour of Mr Bhushan, Z Y
Mrs Shazia and she also has a trapezium-shaped plot. How will h
you find the area of this plot? 1 2
To find the area of this plot, we divide the plot into three parts as W X
shown in the adjoining figure. c L b M d
a
So, area of the plot = area of right triangle 1 + area of a rectangle
+ area of right triangle 2 Quick Check
1 1 Find the area of the
= × ×+ ×+ ××dh following trapeziums.
ch
bh
2 2
1 1. A 16 cm B
= × ×(c + 2b + ) d
h
2 10 cm
1
b
bd
= × × (  c + + ) +  
h

2 D 25 cm C
1
+ )
h
= × ×(a b 2. 7 cm
2
Thus, we can observe that the area of any trapezium is equal to 3 cm
1 ××(a b sq. units.
+ )
h
2 9 cm
Mathematics-8 234