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