Question

Prove that the area of trapezium = half × height × sum of parallel sides

Answer 1

Answer:

Areas of Parallelograms and Triangles. Prove that the area of a trapezium is equal to half of the product of its height and sum of parallel sides. Given: ABCD is a trapezium with AB || CD. ... ∵ In a triangle, the line segment joining the mid-points of any two sides is parallel to the third side.

Step-by-step explanation:

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Answer 2

Answer:

Draw a trapezium say abcd and join the diagonals you will obtain two triangle draw two perpendiculars on diagonals from both parallel sides 

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)

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