# Prove that the area of a trapezium is half the sum of the parallel sides multiplied by the distance between them

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by gajala

plz i want the answer of the question

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by gajala

plz i want the answer of the question

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now area of quadrilateral(trapezium)=sum of area of both the triangles

let a and b be two parallel sides and h be the perpendiculars

area of 1st triangle=1/2 x a x h ....1

area of 2nd triangle=1/2 x b x h .........2

sum of 1 and 2 = area of quadrilateral(trapezium)

1/2 x a x h +1/2 x b x h= area of trapezium

1/2 x (a+b) x h= area of trapezium (taking out 1/2 as common)

thus proved............