Answer:
Perimeter = 24 units
Area = 36 units^2
Step-by-step explanation:
Given
[tex]J=(1,2)[/tex]
[tex]K = (7,2)[/tex]
[tex]L = (7,8)[/tex]
[tex]M = (1,8)[/tex]
Required
Calculate the perimeter and the area
Calculating Perimeter:
First, we calculate the distance between each point.
For J and K
[tex]J=(1,2)[/tex] [tex]K = (7,2)[/tex]
They have the same y value (i.e. 2); So, the distance is the difference between their x values:
[tex]D_1 = |1-7|=|-6| = 6[/tex]
For K and L
[tex]K = (7,2)[/tex] [tex]L = (7,8)[/tex]
They have the same x value (i.e. 7); So, the distance is the difference between their y values:
[tex]D_2 = |2-8| = |-6| = 6[/tex]
For L and M
[tex]L = (7,8)[/tex] [tex]M = (1,8)[/tex]
They have the same y value (i.e. 8); So, the distance is the difference between their x values:
[tex]D_3 = |7-1| = |6| = 6[/tex]
For M and J
[tex]J=(1,2)[/tex] [tex]M = (1,8)[/tex]
They have the same x value (i.e. 1); So, the distance is the difference between their y values:
[tex]D_4 = |2-8| = |-6| = 6[/tex]
So, the perimeter (P) is:
[tex]P = D_1 + D_2 + D_3 + D_4[/tex]
[tex]P = 6 + 6 + 6 + 6[/tex]
[tex]P = 24[/tex]
Calculating the Area
The area is calculated using:
[tex]Area = \frac{1}{2}|(x_1y_2+x_2y_3+x_3y_4+x_4y_1) - (x_2y_1 + x_3y_2+x_4y_3+x_1y_4)|[/tex]
Where:
[tex]J=(1,2)[/tex] -- [tex](x_1,y_1)[/tex]
[tex]K = (7,2)[/tex] -- [tex](x_2,y_2)[/tex]
[tex]L = (7,8)[/tex] -- [tex](x_3,y_3)[/tex]
[tex]M = (1,8)[/tex] -- [tex](x_4,y_4)[/tex]
So, we have:
[tex]Area = \frac{1}{2}|(1*2+7*8+7*8+1*2)-(7*2+7*2+1*8+1*8)|[/tex]
[tex]Area = \frac{1}{2}|(116)-(44)|[/tex]
[tex]Area = \frac{1}{2}|72|[/tex]
[tex]Area = \frac{1}{2}*72[/tex]
[tex]Area = 36[/tex]
