[ Properties and characteristics of an isosceles triangle. ]

[ Pythagorean Theorem (direct and inverse). ]

The lateral sides of a right trapezoid are 10 and 8. The diagonal of the trapezoid, drawn from the vertex of the acute angle, bisects this angle.

Find the area of the trapezoid.
Let the acute angle at vertex $D$ of the rectangular trapezoid $A B C D$ with bases $A D$ and $B C$ be bisected by the diagonal $B D$, and $A B=8$ and

$C D=10$. Triangle $B C D$ is isosceles because $\angle C B D=\angle B D A=\angle C D B$, so $B C=C D=10$.

Drop the height $C H$ to the base $A D$. Since $A B C H$ is a rectangle, $C H=A B=8$ and $A H=B C=10$. From the right triangle $C D H$, we find that $D H=6$, so

$$
A D=A H+D H=16 . \text { Therefore, } S_{A B C D}=1 / 2(A D+B C) \cdot C H=1 / 2(16+10) \cdot 8=104 .
$$

## Answer

104.