Question

find the area of the polygon.
41 square units
44 square units
52 square units
56 square units

Explanation:

Step1: Divide the polygon

Divide the polygon into a triangle and a rectangle. The rectangle has vertices \(C(2,5)\), \(D(2,9)\), \(E(6,9)\), \(A(6,0)\) and the triangle has vertices \(B(- 3,5)\), \(C(2,5)\), \(A(6,0)\).

Step2: Calculate the area of the rectangle

The length of the rectangle along the \(y -\)axis is \(9 - 5=4\) units and along the \(x -\)axis is \(6 - 2 = 4\) units. Using the formula for the area of a rectangle \(A_{r}=l\times w\), we have \(A_{r}=4\times4 = 16\) square units.

Step3: Calculate the base and height of the triangle

The base of the triangle (distance between \(B(-3,5)\) and \(C(2,5)\)) is \(2-(-3)=5\) units. The height of the triangle (perpendicular distance from \(A(6,0)\) to the line \(y = 5\)) is \(5\) units. Using the formula for the area of a triangle \(A_{t}=\frac{1}{2}\times b\times h\), we get \(A_{t}=\frac{1}{2}\times5\times5=\frac{25}{2}=12.5\) square units.

Step4: Calculate the total area of the polygon

The total area \(A = A_{r}+A_{t}\). \(A=16 + 25=41\) square units.

Answer:

A. 41 square units