### 10.370 The larger of the parallel sides of a trapezoid is equal to $a$, the smaller is equal to $b$, the non-parallel sides are equal to $c$ and $d$. Find the area of the trapezoid.
## Solution.

$$
=\frac{2 b \cdot S_{K C D}}{a-b} \Rightarrow S_{A B C D}=\begin{aligned}
& \text { Let } A B C D-\text { the given trapezoid, } \\
& \begin{array}{l}
A D=a ; B C=b, A B=c, C D=d, h-\text { height } \\
\text { of the trapezoid. Draw } C K \| A B . \\
\text { Then } K D=a-b, C K=c
\end{array} \\
& h=\frac{2 S_{K C D}}{a-b}, S_{A B C K}=h \cdot A K= \\
& D
\end{aligned}
$$

In the end, we have

Answer: $\frac{a+b}{4(a-b)} \cdot \sqrt{(a+c+d-b)(a+d-b-c)(a+c-b-d)(b+c+d-a)}$.