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If $ h=10 \mathrm{cm}, c=6 \mathrm{cm}, b=12 \mathrm{cm}, d=4 \mathrm{cm}, $ find the values of each of its parts separately and add to find the area WXYZ. Verify it by putting the values of $ h, a $ and $ b $ in the expression $ \frac{h(a+b)}{2} $.
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Given : In the above figure, h=10cm,c=6cm,b=12cm,d=4cm

To do : Find area of Trapezium using two different methods.

By dividing the trapezium into separate parts:

Area of trapezium WXYZ = Area of triangle with base'c'+area of rectangle +area of triangle with base 'd'

=(12×c×h)+(b×h)+(12×d×h)

=(12×6×10)+(12×10)+(12×4×10)

=(30)+(120)+(20)

=170cm2

By using the given expression:

Here a = b + c + d

= 12 + 6 + 4

=22 cm

Area of WXYZ as per the expression h(a+b)2

=10(22+12)2

=10(34)2

=10×17

=170cm2

From both methods, we got same answer. Hence, verified

Updated on: 10-Oct-2022

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