Question

5 darius and his stepdad play music at an outdoor charity concert. the stage is shaped like the polygon shown. what is the area of the stage? show your work.

Explanation:

Step1: Divide the polygon into simpler shapes

Divide the polygon into a rectangle and a trapezoid. The rectangle has length 9m and width 5m. The trapezoid has bases \(b_1 = 3m\) and \(b_2=9m\) and height \(h = 1.5m\).

Step2: Calculate the area of the rectangle

The area formula for a rectangle is \(A_{rect}=l\times w\). Here, \(l = 9m\) and \(w = 5m\), so \(A_{rect}=9\times5=45m^{2}\).

Step3: Calculate the area of the trapezoid

The area formula for a trapezoid is \(A_{trap}=\frac{(b_1 + b_2)h}{2}\). Here, \(b_1 = 3m\), \(b_2 = 9m\) and \(h=1.5m\). So \(A_{trap}=\frac{(3 + 9)\times1.5}{2}=\frac{12\times1.5}{2}=9m^{2}\).

Step4: Calculate the total area of the polygon

The total area \(A = A_{rect}+A_{trap}\). So \(A=45 + 9=54m^{2}\).

Answer:

\(54m^{2}\)