Question #eb0f0

2 Answers
Jan 28, 2018

Perimeter of pentagon #color(green)(P = 17.8)#

Explanation:

Perimeter of pentagon = Sum of the lengths of the five sides of the pentagon.

Let the five sides be a, b, c, d, e.

Using the formula of distance between 2 points,

#a = sqrt((0-2)^2 + (3-3)^2) = 2#

#b = sqrt((2-2)^2 + (3-0)^2) = 3#

c = sqrt((2-1)^2 + (0+4)^2) = sqrt17 = 4.1#

d = sqrt((1+2)^2 + (-4+1)^2) = sqrt18 = 4.2#

#e = sqrt((-2-0)^2 + (-1-3)^2) = sqrt20 = 4.5#

Perimeter of pentagon #P = 2 + 3 + 4.1 + 4.2 + 4.5 = color(green)(17.8)#

Jan 28, 2018

Perimeter of the polygon is #17.8# unit.

Explanation:

Vertices of the polygon are

#A(0,3),B(2,3),C(2,0),D(1,-4),E(-2,-1)#.

Length formula #L= sqrt ((x_1-x_2)^2+(y_1-y_2)^2#

#AB= sqrt ((0-2)^2+(3-3)^2) = 2.0# unit

#BC= sqrt ((2-2)^2+(3-0)^2) = 3.0# unit

#CD= sqrt ((2-1)^2+(0+4)^2) = sqrt17~~4.12# unit

#DE= sqrt ((1+2)^2+(-4+1)^2) = sqrt18~~4.24# unit

#EA= sqrt ((-2-0)^2+(-1-3)^2) = sqrt20~~4.47# unit

Perimeter of the polygon is #P=AB+BC+CD+DE+EA#

or #P=2.0+3.0+4.12+4.24+4.47= 17.83# unit

Perimeter of the polygon is#17.8# unit [Ans]