Question

the area of a trapezium is 'a' and its parallel sides are x and y the distance between it's parallel sides is ? ( please step by step explanation)​

Answer 1

Consider the trapezium ABCD with with AB∣∣CD

∴AP=BQ=h(say) [distance between parallel lines one equal]

ar(ABCD)=ar(△ADC)+ar(△ABC)(1)

ar(△ADC)=

2

1

×base×height=

2

1

×(DC)×h(2)

ar(△ABC)=

2

1

×base×height=

2

1

×(AB)×h(3)

From (1),(2)and (3)

ar(ABCD)=

2

1

×h(CD)+

2

1

×h(AB)

ar(△ABCD)=

2

1

h[AB+CD]

∴ Area of a trapezium is half the product of the sum of parallel sides and distance between the parallel sides.

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