Answer:
A. 10.8.
Step-by-step explanation:
We are given that a shape ABCD . The point A is (7,5), B (6,3), C(3,2) and D (4,4).
By using distance formula we find sides of given shape and then find perimeter.
Distance formula:The distance between two points [tex](x_1,y_1)[/tex]and [tex](x_2,y_2)[/tex]
=[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Length of side AB=[tex]\sqrt{(6-7)^2+(3-5)^2}=\sqrt{1+4}[/tex]
Length of side AB=[tex]\sqrt5[/tex]units
Length of BC=[tex]\sqrt{(3-6)^2+(2-3)^2}=\sqrt{9+1}[/tex]
Length of side BC=[tex]\sqrt{10}[/tex] units
Length of side CD=[tex]\sqrt{(4-3)^2+(4-2)^2}=\sqrt{1+4}[/tex]
Length of side CD=[tex]\sqrt5[/tex]
Length of side AD=[tex]\sqrt{(4-7)^2+(4-5)}=\sqrt{9+1}[/tex]
Length of side AD=[tex]\sqrt{10}[/tex]
Therefore, the perimeter of given shape ABCD=AB+BC+CD+AD
The perimeter of given shape ABCD=[tex]\sqrt5+\sqrt{10}+\sqrt5+\sqrt{10}[/tex]
The perimeter of given shape ABCD=[tex]2\sqrt5+2\sqrt{10}=2\times 2.23+2\times 3.16[/tex].
Substitute [tex]\sqrt5=2.23,\sqrt{10}=3.16[/tex]
The perimeter of given shape=4.46+6.32
The perimeter of given shape=10.78=10.8(round off)
Hence, the perimeter of given shape=10.8 units
Therefore, option A is correct.
