Question

Area of a trapezium whose parallel sides are of lengths 40 metres and 24 metres and whose non- parallel sides are equal, each being 10 metres is​

Answer 1

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Answer 2

Given :-

• Parallel sides of trapezium are 40 m and 24 m

• Non parallel sides of trapezium are 10 m each

Solution :-

Draw DP|| AD So that it can complete the parallelogram ABPD

BP = AD = 10cm [ Given ]

AB = DP = 24m

[ Opposite sides of parallelogram are equal ]

PC = DC - DP

PC = 40 - 24 = 16cm

In ΔBPC

Semi perimeter = a + b + c / 2

S = 10 + 10 + 16 / 2

S = 36 / 2

S = 18cm

Area of ΔBPC

By using Heron's formula

$\sqrt{s \: ( \: s \: - \: a \: ) \: ( \: s - b \: ) \: ( \: s \: - \: c \: ) }$

Put the required values,

$\sqrt{18 \: ( 18 -10 )(18 - 10 )( \: 18 -16 ) } \\ = \sqrt{18 \times 8 \times 8 \times 2} \\ = \sqrt{3 \times 3 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 } \\ = 3 \times 2 \times 2 \times 2 \times 2 \\ = 48m^2$

Thus,

Area of triangle = 48 m^2

Now,

As we know that,

Area of triangle = 1/2 * b * h

Put the required values,

48 = 1/2 * 16 * h

h = 48/8

h = 6m

Area of trapezium = 1/2 ( a + b) * h

Put the required values,

Area of trapezium = 1/2 * ( 40 + 24 ) * 6

Area of trapezium = 1/2 * 64 * 6

Area of trapezium = 32 * 6

Area of trapezium = 192 m^2