### Theory:

Area of trapezium: To obtain the area of a trapezium, multiply the sum of the bases by the height and then divide by $$2$$.

The area of a trapezium is computed with the following formula:

Area of trapezium $$=$$ $\frac{1}{2}×\left(a\phantom{\rule{0.147em}{0ex}}+b\right)×\left(h\right)$ square units.

(where $$a$$ and $$b$$ is bases (parallel sides) and $$h$$ is leg or height (between the non-parallel sides)).

Area of the trapezium $$ABCD$$:

Proof: Area of a trapezium $$ABCD$$.

Area of trapezium $$ABCD$$ $$=$$ $\frac{1}{2}\left(\mathit{AB}+\mathit{DC}\right)×\left(h\right)$ $$square units$$.

$$=$$ area of triangle $\left(\mathit{DEA}\right)$ $$+$$ area of rectangle $\left(\mathit{DEFC}\right)$ $$+$$ area of triangle $\left(\mathit{CFB}\right)$

$$=$$ $\frac{1}{2}×\mathit{AE}×\mathit{DE}$ $$+$$ $\mathit{DE}×\mathit{EF}$ $$+$$ $\frac{1}{2}×\mathit{FB}×\mathit{CF}$

$$=$$ $\frac{1}{2}×\mathit{AE}×h$ $$+$$ $h×\mathit{EF}$ $$+$$ $\frac{1}{2}×\mathit{FB}×h$

$$=$$ $\frac{1}{2}×\left(\mathit{AE}+2\mathit{EF}+\mathit{FB}\right)×h$

$$=$$ $\frac{1}{2}×\left(\mathit{AE}+\mathit{EF}+\mathit{CD}+\mathit{FB}\right)×h$

$$=$$ $\frac{1}{2}×\left(\mathit{AE}+\mathit{EF}+\mathit{FB}+\mathit{CD}\right)×h$

$$=$$ $\frac{1}{2}×\left(\mathit{AB}+\mathit{CD}\right)×\left(h\right)\phantom{\rule{0.147em}{0ex}}$

$$=$$ $\frac{1}{2}×\left(a\phantom{\rule{0.147em}{0ex}}+b\right)×\left(h\right)$

$$=$$ $$\frac{1}{2}\times$$($$\text{sum of parallel side}$$) $$\times$$$$(\text{height})$$ square units.

Therefore, Area of trapezium $$ABCD =$$ $\frac{1}{2}×\left(a\phantom{\rule{0.147em}{0ex}}+b\right)×\left(h\right)$ or

Perimeter of trapezium: The Perimeter is the sum of all side lengths.

The perimeter of a trapezium is computed with the following formula:

Perimeter of trapezium $$=$$ $$a + b + c + d$$ (where $$a$$, $$b$$ are denoted as bases (parallel sides) and $$c$$, $$d$$ are denoted as legs (non-parallel sides)).