Площа трапеції

In this trapezoid, sides $CB$ and $AD$ are parallel, and all the angles depicted by box angles are right. Segments $XC$ and $YB$ are not necessarily equal in length. Let's call the height(length of $AX$ or $YD$) $h$.

To find the area of this trapezoid, we first find the area of the right - triangles: $\bigtriangleup XCA$ and $\bigtriangleup YBD$.

Those areas are $h * XC/2$ and $h * YB/2$.

Adding these areas, we get: $h(XC + YB)/2$.

Then, find the area of rectangle $XADY$, which is $AD$ * h.

$h(XC + YB)/2 + h(AD)$ is the area of our trapezoid.

Simplifying that, we have:

$h(XC + YB)/2 + h(2AD)/2$,

and $h(XC + YB + 2AD)/2$

Since $AD$ is equal to $XY$, we can substitute the second $AD$ for it, obtaining:

$h(XC + XY + YB + AD)/2$, which can simplify to $h(CB + AD)/2$.

This final area formula is often said as the height of the trapezoid multiplied by the average of the two bases.

This formula certainly works on all the types of trapezoids in the world.

Good luck!

The area of a trapezoid is the average of the bases times the height. In mathematical terms, it is $\frac{b_1+b_2}{2}h$, where $b_1$ and $b_2$ are the bases and $h$ is the height. Here is a worksheet to practice your skills. You can think of the area of a rectangle as a specific case of the trapezoid where $b_1$ and $b_2$ are equal. Best of luck!