Question

what is the area of the composite figure? a 6 square units b 7 square units c 8 square units d 9 square units

Explanation:

Step1: Identify component shapes

The composite figure is composed of a triangle and a rectangle.

Step2: Calculate rectangle area

The rectangle has length $l = 3$ (from $x=- 2$ to $x = 1$) and width $w=2$. The area formula for a rectangle is $A_{r}=l\times w$. So $A_{r}=3\times2 = 6$.

Step3: Calculate triangle area

The triangle has base $b = 3$ (from $x=-2$ to $x = 1$) and height $h = 2$ (from $y = 2$ to $y = 4$). The area formula for a triangle is $A_{t}=\frac{1}{2}\times b\times h$. So $A_{t}=\frac{1}{2}\times3\times2=3$.

Step4: Calculate total area

The total area $A$ of the composite figure is the sum of the rectangle and triangle areas, $A=A_{r}+A_{t}=6 + 3=9$.

Answer:

D. 9 square units