Question

Find the perimeter of quadrilateral ABCD. Round your answer to the nearest hundredth.

A(-5, 4)
B(0,3)
C(4,-1)
D(4,-5)
E(2,-3)
F(-2,1)​

Answer 1

The perimeter of quadrilateral ABCD is 27.48 units

Explanation:

we know that

The perimeter of quadrilateral ABCD is the sum of its four length sides

so

`P=AB+BC+CD+AD`

we have

A(-5, 4),B(0,3),C(4,-1) and D(4,-5)

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

Find the distance AB

Substitute in the formula

`d=\sqrt{(3-4)^(2)+(0+5)^(2)}`

`d=\sqrt{(-1)^(2)+(5)^(2)}`

`AB=√(26)\ units`

Find the distance BC

Substitute in the formula

`d=\sqrt{(-1-3)^(2)+(4-0)^(2)}`

`d=\sqrt{(-4)^(2)+(4)^(2)}`

`BC=√(32)\ units`

Find the distance CD

Substitute in the formula

`d=\sqrt{(-5+1)^(2)+(4-4)^(2)}`

`d=\sqrt{(-4)^(2)+(0)^(2)}`

`CD=4\ units`

Find the distance AD

Substitute in the formula

`d=\sqrt{(-5-4)^(2)+(4+5)^(2)}`

`d=\sqrt{(-9)^(2)+(9)^(2)}`

`AD=√(162)\ units`

Find the perimeter

substitute the values

`P=√(26)+√(32)+4+√(162)=27.48\ units`

see the attached figure to better understand the problem