The diagram shows a garden plot. The area of the garden is ____ square feet. The length of fencing required to completely enclose the garden is_____ feet.
The garden area is given by: [tex]A = \frac{1}{2}(AB + DC)(AD) [/tex] Substituting values we have: [tex]A = \frac{1}{2}(12+6)(8) [/tex] Rewriting we have: [tex]A = \frac{1}{2}(18)(8) [/tex] [tex]A= 72[/tex] The perimeter is given by the sum of the sides. We have then: [tex]
P = AB + AD + DC + CB[/tex] Where, CB is given by: [tex]CB = \sqrt{(16-10)^2 + (12-4)^2} [/tex] [tex]CB = \sqrt{100} [/tex] [tex]CB = 10[/tex] Substituting values: [tex]P=12+8+6+10[/tex] [tex]P=36[/tex] Answer: The area of the garden is 72 square feet. The length of fencing required to completely enclose the garden is 36 feet.
