Question

finding the area of a trapezoid in the coordinate plane. the height, ce, of the trapezoid is 5 units. what is the area of the trapezoid? ad = units. bc = units. the area of the trapezoid is square units. d(0, 13) e(4, 10) c(1, 6) b(5, 3) a(16, 1)

Explanation:

Step1: Calculate length of AD

Use distance formula for two - points \(D(0,13)\) and \(A(16,1)\). \(AD=\sqrt{(16 - 0)^2+(1 - 13)^2}=\sqrt{16^2+( - 12)^2}=\sqrt{256 + 144}=\sqrt{400}=20\)

Step2: Calculate length of BC

Use distance formula for two - points \(B(5,3)\) and \(C(1,6)\). \(BC=\sqrt{(1 - 5)^2+(6 - 3)^2}=\sqrt{( - 4)^2+3^2}=\sqrt{16 + 9}=\sqrt{25}=5\)

Step3: Calculate area of trapezoid

The area formula of a trapezoid is \(A=\frac{(b_1 + b_2)h}{2}\), where \(b_1\) and \(b_2\) are the lengths of the parallel sides and \(h\) is the height. Here \(b_1 = AD = 20\), \(b_2=BC = 5\) and \(h = 5\). So \(A=\frac{(20 + 5)\times5}{2}=\frac{25\times5}{2}=\frac{125}{2}=62.5\)

Answer:

AD = 20 units
BC = 5 units
The area of the trapezoid is 62.5 square units