Question

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

Explanation:

Step1: Find the length of PS

In right - triangle PSK, using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = SK = 13\) and \(b = PK = 12\). Let \(a=PS\). Then \(PS=\sqrt{SK^{2}-PK^{2}}=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}=5\).

Step2: Calculate the area of the trapezoid

The formula for the area 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. Here, the parallel sides are \(ST = 8\) and \(PK = 12\), and the height \(PS = 5\). So \(A=\frac{(8 + 12)\times5}{2}=\frac{20\times5}{2}=50\).

Answer:

50