### Theory:

To calculate the area of a trapezium, we have to multiply the sum of the parallel sides with a perpendicular distance between them and divide by $$2$$.

Area of a trapezium $$A$$ $$=$$ $\frac{1}{2}$($$a + b$$)$$×h$$ square units.

Where $$A$$ is the area of the trapezium, '$$a$$' and '$$b$$' is the length of the parallel sides, and '$$h$$' is the perpendicular distance between the parallel sides.
Let us derive the formula for the area of trapezium by splitting the trapezium into two triangles.

To prove the area of a trapezium $$A =$$ $\frac{1}{2}$ ($$a + b$$)$$×h$$ square units.

We know that, Area of trapezium $$ABCD =$$ Area of $$Δ ABD$$ $$+$$ Area of $$ΔCBD$$.

Now, find the area of $$ΔABD$$ and the area of $$ΔBCD$$ separately and add them to get the area of trapezium.

Area of $$ΔABD$$ $$+$$ Area of $$ΔCBD =$$ $\frac{1}{2}$ $$b × h$$ $$+$$ $\frac{1}{2}$ $$b × h$$.

From the above figure, the base of $$ΔABD =$$ $$a$$ and the base of $$ΔCBD =$$ $$b$$

Also, the height of the triangles, $$ΔABD = ΔCBD = h$$.

Substitute the known value.

Area of trapezium $$ABCD =$$$\frac{1}{2}$ $$b × h$$ $$+ a × h$$.

Taking $$h$$ commonly outside gives:

$$=$$ $\frac{1}{2}$ ($$a + b$$)$$× h$$
Thus, the area of the trapezium $$ABCD =$$ $\frac{1}{2}$ ($$a + b$$)$$×h$$ square units.