Question

solve the following problems. given: pstk is a trapezoid, m∠p = 90°, sk = 13, pk = 12, st = 8. find: the area of pstk

Explanation:

Step1: Find the length of PS using the Pythagorean theorem

In right - triangle PSK, by the Pythagorean theorem \(PS=\sqrt{SK^{2}-PK^{2}}\). Given \(SK = 13\) and \(PK = 12\), then \(PS=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}=5\).

Step2: Use the trapezoid area formula

The area formula of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a\) and \(b\) are the lengths of the parallel sides and \(h\) is the height. In trapezoid PSTK, the parallel sides are \(ST\) and \(PK\), with \(ST = 8\), \(PK = 12\), and the height \(PS = 5\). So \(A=\frac{(8 + 12)\times5}{2}\).
\[

$$\begin{align*} A&=\frac{20\times5}{2}\\ &=50 \end{align*}$$

\]

Answer:

50