Answer:
Option 2 - 15.7 unit.
Step-by-step explanation:
Given : The image attached.
To find : The perimeter of the following shape?
Solution :
First we determine the coordinate of points,
A=(5,5)
B=(7,3)
C=(3,0)
D=(1,2)
Now, We apply distance formula to find the length of the sides.
\(D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
The distance between AB,
\(AB=\sqrt{(7-5)^2+(3-5)^2}\)
\(AB=\sqrt{(-2)^2+(2)^2}\)
\(AB=\sqrt{4+4}\)
\(AB=\sqrt{8}\)
The distance between BC,
\(BC=\sqrt{(3-7)^2+(0-3)^2}\)
\(BC=\sqrt{(-4)^2+(-3)^2}\)
\(BC=\sqrt{16+9}\)
\(BC=\sqrt{25}\)
\(BC=5\)
The distance between CD,
\(CD=\sqrt{(1-3)^2+(2-0)^2}\)
\(CD=\sqrt{(-2)^2+(2)^2}\)
\(CD=\sqrt{4+4}\)
\(CD=\sqrt{8}\)
The distance between DA,
\(DA=\sqrt{(5-1)^2+(5-2)^2}\)
\(DA=\sqrt{(4)^2+(3)^2}\)
\(DA=\sqrt{16+9}\)
\(DA=\sqrt{25}\)
\(DA=5\)
The perimeter of the given shape is
\(P=AB+BC+CD+DA\)
\(P=\sqrt{8}+5+\sqrt{8}+5\)
\(P=2\sqrt{8}+10\)
\(P=4\sqrt{2}+10\)
\(P=4(1.41)+10\)
\(P=5.64+10\)
\(P=15.64\)
\(P\approx15.7\)
Therefore, Option 2 is correct.
The perimeter of the given shape is 15.7 unit.
