Question

Find the perimeter of the following shape, rounded to the nearest tenth:

Answer 1

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.

Answer 2

So will be 5+5 + 2sqrt2 +2sqrt2 = 10 + 3 +3 = 16 rounded 

hope helped