Question

PLEASE HELP ME:

Find the perimeter of the figure. Round to the nearest tenth.

Answer 1

perimeter = 20.9 units

Explanation:

perimeter

perimeter = distance around two dimensional shape

= addition of all sides lengths

perimeter of the figure

= AB+BC+CD+AD

distance formula:

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

1) distance of AB

A(-3,0) B(2,4)

x1 = -3 x2 = 2

y1 = 0 y2 = 4

(substitute the values into the distance formula)

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

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

`ab = √(41)`AB = 6.4 units

2) distance of BC

B(2,4) C(3,1)

x1 = 2 x2 = 3

y1 = 4 y2 = 1

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

`bc = \sqrt{1 {}^(2) + ( - 3) {}^(2) }`

`bc = √(10)`

BC = 3.2 units

3) distance of CD

C(3,1) D(-4,-3)

x1 = 3 x2 = -4

y1 = 1 y2 = -3

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

`cd = \sqrt{( - 7) {}^(2) + ( - 4 ){}^(2) }`

`cd = √(65)`

CD = 8.1 units

4) distance of AD

A(-3,0) D(-4,-3)

x1 = -3 x2 = -4

y1 = 0 y2 = -3

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

`ad = \sqrt{( - 1) {}^(2) + ( - 3) {}^(2) }`

`ad = √(10)`

AD = 3.2 units

perimeter of figure

= AB+BC+CD+AD

= 6.4 + 3.2 + 8.1 + 3.2

= 20.9 units