A3. The area of a trapezoid with sides $a=17, b=15, c=3$ and $d=13$
(A) is 120
(B) is 132
(C) is 156
(D) is 192
(E) is not determined, as its height is unknown
A3. Let $v$ be the height of the trapezoid. By the Pythagorean theorem (see the figure), we have $v^{2}=15^{2}-y^{2}$ and $v^{2}=13^{2}-x^{2}$. Since $x+y+3=17$, it follows that $y=14-x$ and thus $15^{2}-(14-x)^{2}=13^{2}-x^{2}$, from which we get $x=5$. Therefore, $v=\sqrt{13^{2}-5^{2}}=12$. The area of the trapezoid is $\frac{v(a+c)}{2}=120$.

![](https://cdn.mathpix.com/cropped/2024_06_07_c1f0ff7099009a973f5fg-12.jpg?height=434&width=468&top_left_y=2239&top_left_x=314)