Question

Prove that area of trapezium​

Answer 1

Answer:

Prove that area of a trapezium is equal to half the product of the sum of parallel sides and distance between the parallel sides.

Medium

ANSWER

Consider the trapezium ABCD with with AB∣∣toCD

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

ar(ABCD)=ar(△ADC)+ar(△ABC)

.....(2)

ar(△ADC)=

2

1

×base×height=

2

1

×(DC)×h

......(1)

ar(△ABC)=

2

1

×base×height=

2

1

×(AB)×h

.....(3)

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

ar(ABCD)=

2

1

×h(CP)+

2

h(AB)ar(△ABCD)= 21 h[AB+CD] ∴

areaoftrapezium=halfofproductheightofheightandsumofparallelsides.