$20 \cdot 96$ An isosceles trapezoid is circumscribed about a circle, the longer base is 16, and one of the base angles is $\arcsin 0.8$. Then the area of the trapezoid is
(A) 72.
(B) 75.
(C) 80.
(D) 90.
(E) Not uniquely determined.
(39th American High School Mathematics Examination, 1988)
[Solution] Let the trapezoid be $ABCD$, and $\angle B=\arcsin 0.8$. Without loss of generality, assume $AH=8x, AB=$ $10x$, then
$$
BH=6x. \text{ (if there is a figure) }
$$

Since the trapezoid is circumscribed around a circle, then
$$
AD + BC = AB + CD,
$$

Thus $(16-12x) + 16 = 10x + 10x$,
we get $x=1$,
$$
\begin{array}{r}
\therefore AH=8, AD=16-2 \cdot 6=4, \text{ then } \\
\quad S_{ABCD}=\frac{1}{2} \cdot (4+16) \cdot 8=80.
\end{array}
$$

Therefore, the answer is $(C)$.