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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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Academic Mathematics NCERT Class 8

Problem Statement

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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Solution

Given : In the above figure,

h = 10 c m, c = 6 c m, b = 12 c m, d = 4 c m

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'

=

(\frac{1}{2} \times c \times h) + (b \times h) + (\frac{1}{2} \times d \times h)

=

(\frac{1}{2} \times 6 \times 10) + (12 \times 10) + (\frac{1}{2} \times 4 \times 10)

=

(30) + (120) + (20)

=

170 c m^{2}

By using the given expression:

Here a = b + c + d

= 12 + 6 + 4

=22 cm

Area of WXYZ as per the expression

\frac{h (a + b)}{2}

=

\frac{10 (22 + 12)}{2}

=

\frac{10 (34)}{2}

=

10 \times 17

=

170 c m^{2}

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

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Updated on: 10-Oct-2022

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