By dividing a trapezium into two triangles show that its area is, half the sum of the parallel sides multiplied Class 9

By dividing a trapezium into two triangles show that its area is, half the sum of the parallel sides multiplied Class 9

Question 1.

By dividing a trapezium into two triangles show that its area is, half the sum of the parallel sides multiplied by the height (the same formula as the one given above). Class 9

Solution:

Given:

In trapezium,

Parallel sides = a, b, height = h

To prove:

Area of trapezium = $\frac{1}{2}$(a + b)h

Construction: Draw a diagonal to divide the trapezium into two triangles.

Proof:

∴ For triangle 1:

Base = a, height = h

∴ Area of triangle = $\frac{1}{2}$ah

For triangle 2:

∵ Base = b, height = h

∴ Area of triangle = $\frac{1}{2}$bh ...(ii)

∵ Area of trapezium

= sum of areas of two triangles

$\begin{aligned} & =\frac{1}{2} a h+\frac{1}{2} b h \quad \ldots[\text { From (i) and (ii) }] \\ & =\frac{1}{2}(a+b) h\end{aligned}$

∴ Area of trapezium = $\frac{1}{2}$ (a + b)h