Question

what is the area of the composite figure? 1080 square units 810 square units 742.5 square units 125 square units

Explanation:

Step1: Divide the composite figure

Divide the figure into a rectangle and a triangle.

Step2: Calculate rectangle area

The rectangle has length \(l = 45\) (from \(x=- 15\) to \(x = 30\)) and width \(w=18\) (from \(y = 0\) to \(y = 18\)). The area of a rectangle \(A_{r}=l\times w\), so \(A_{r}=45\times18 = 810\) square - units.

Step3: Calculate triangle area

The base of the triangle \(b = 30\) (from \(x = 0\) to \(x = 30\)) and height \(h = 18\) (from \(y=-18\) to \(y = 0\)). The area of a triangle \(A_{t}=\frac{1}{2}\times b\times h\), so \(A_{t}=\frac{1}{2}\times30\times18=270\) square - units.

Step4: Calculate total area

The area of the composite figure \(A = A_{r}+A_{t}\). So \(A=810 + 270=1080\) square - units.

Answer:

1080 square units