Question

What is the perimeter of polygon ABCD?fyА121110B98765432.138910 11 12 13

Answer 1

Looking at the polygon above, we have divided it into different right-angle triangle segments to be able to get the length of AD, AB,BC, CD

The addition of all these lengths will give us the perimeter of the polygon ABCD.

We will find the length of these sides using Pythagoras theorem?

Length AD is:

`\begin{gathered} AD=\sqrt[]{12^2+5^2} \\ =\sqrt[]{144+25} \\ =\sqrt[]{169} \\ =13\text{units} \end{gathered}`

The length of AB is:

`\begin{gathered} AB=\sqrt[]{3^2+4^2} \\ =\sqrt[]{9+16} \\ =\sqrt[]{25} \\ =5\text{units} \end{gathered}`

The length of BC is:

`\begin{gathered} BC=\sqrt[]{4^2+3^2} \\ =\sqrt[]{16+9} \\ =\sqrt[]{25} \\ =5\text{ units} \end{gathered}`

The length of CD is:

`\begin{gathered} CD=\sqrt[]{5^2+12^2} \\ =\sqrt[]{25+144} \\ =\sqrt[]{169} \\ =13\text{ units} \end{gathered}`

The perimeter of the polygon will be calculated thus: