Answer:
[tex]Area = 10[/tex]
Step-by-step explanation:
Given
[tex]A = (2,1)[/tex]
[tex]B =(4,7)[/tex]
[tex]C =(6,3)[/tex]
Required
The area of the park
The outline is a triangle and as such, the area is calculated using:
[tex]Area = \frac{1}{2}|(x_1y_2 - x_2y_1) + (x_2y_3 - x_3y_2) + (x_3y_1 - x_1y_3)|[/tex]
This gives:
[tex]Area = \frac{1}{2}|(2*7 - 4*1) + (4*3 - 6*7) + (6*1 - 2*3)|[/tex]
Using a calculator, we have:
[tex]Area = \frac{1}{2}|-20|[/tex]
Remove absolute bracket
[tex]Area = \frac{1}{2}*20[/tex]
[tex]Area = 10[/tex]
