Question

Why do we add bases of a trapezoid, while finding its area?

Answer 1

Bases of a trapezoid need to be added in the formula as for deriving the formula, we have split trapezium in two triangles with different bases but common height.

Explanation:

Let us consider the trapezium `ABCD` as drawn below, with parallel sides as `a` and `b` and height as `h`.

We have joined `BD` dividing the trapezium in two `DeltasABD" and "BCD` and have also drawn a perpendicular from `D` on `AB` and from `B` on `DC` extended.

As area of a triangle is `1/2xx"Base"xx"Height"`, as `AB`||`CD`, height `h` of the two triangles is same,

but as it is a trapzeium, the base of two triangles are different and hence while

area of `DeltaABD=1/2xxaxxh`

area of `DeltaBCD-1/2xxbxxh`

and therefore, area of trapezium is `1/2xxaxxh+1/2xxbxxh`

or `1/2xx(a+b)xxh`

Hence, bases of a trapezoid need to be added in the formula as for deriving the formula, we have split trapezium in two triangles with different bases but common height.