Question

type the correct answer in each box. 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.

Explanation:

Step1: Find the coordinates of points

Assume \(A=(3,12)\), \(B=(15,12)\), \(C=(10,4)\), \(D=(3,4)\)

Step2: Calculate the lengths of sides

• \(AD = 12 - 4=8\)
• \(DC=10 - 3 = 7\)
• \(AB=15 - 3=12\)
• For \(BC\), use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \(x_1 = 10,y_1 = 4,x_2 = 15,y_2 = 12\), so \(BC=\sqrt{(15 - 10)^2+(12 - 4)^2}=\sqrt{25 + 64}=\sqrt{89}\approx9.43\)

Step3: Calculate the area of the trapezoid

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a = DC = 7\), \(b = AB=12\), \(h = AD = 8\). So \(A=\frac{(7 + 12)\times8}{2}=\frac{19\times8}{2}=76\)

Step4: Calculate the perimeter

Perimeter \(P=AD + DC+CB + BA\). \(AD = 8\), \(DC = 7\), \(CB\approx9.43\), \(BA = 12\). So \(P=8 + 7+9.43+12=36.43\)

Answer:

The area of the garden is \(76\) square feet. The length of fencing required to completely enclose the garden is approximately \(36.43\) feet.