Question

What is the best approximation for the perimeter of the pentagon abcde

Answer 1

Answer: Out of the options on the online quiz the answer is 22 units

Step-by-step explanation: I got it right on the test

Answer 2

The perimeter of the pentagon ABCDE is given by:

`P=AB+BC+CD+DE+EA`

From the figure, we can calculate the length of each side:

`\begin{gathered} AB=√(4^2+1^2)=√(17) \\ \\ BC=√(1^2+3^2)=√(10) \\ \\ CD=√(6^2+3^2)=3√(5) \\ \\ DE=√(1^2+3^2)=√(10) \\ \\ EA=√(2^2+4^2)=2√(5) \end{gathered}`

Finally, the perimeter is:

`\begin{gathered} P=√(17)+√(10)+3√(5)+√(10)+2√(5)=√(17)+2√(10)+5√(5) \\ \\ \therefore P\approx21.628 \end{gathered}`