Question

all segments of the polygon meet at right angles (90 degrees). the length of segment \\( \overline { a b } \\) is 10. the length of segment \\( \overline { b c } \\) is 8. the length of segment \\( \overline { d e } \\) is 3. the length of segment \\( \overline { g h } \\) is 2. find the perimeter of the polygon.

Explanation:

Step1: Analyze the horizontal sides

The total length of the horizontal sides is \(2\times10 + 2\times2= 24\).

Step2: Analyze the vertical sides

The total length of the vertical sides is \(2\times8+2\times3 = 22\).

Step3: Calculate the perimeter

The perimeter \(P\) of the polygon is the sum of all side - lengths. Using the formula \(P=(sum\ of\ horizontal\ sides)+(sum\ of\ vertical\ sides)\), we have \(P = 24+22\).

Answer:

\(46\)