Answer:
[tex]31\:\text{square units}[/tex]
Step-by-step explanation:
We can break the composite figure into two triangles and two trapezoids. The area of a triangle is given by [tex]A=\frac{1}{2}bh[/tex] and the area of a trapezoid is given by [tex]A=\frac{b_1+b_2}{2}\cdot h[/tex] (average of the bases multiplied by the height).
Area of first triangle (larger triangle to the figure's left): [tex]\frac{1}{2}\cdot 4\cdot 4=8[/tex]
Area of second triangle (smaller triangle to the figure's right ): [tex]\frac{1}{2}\cdot 2\cdot 5=5[/tex]
Area of first trapezoid (smaller trapezoid directly underneath second triangle and adjacent to both triangles): [tex]4\cdot 2 =8[/tex]
Area of first triangle (larger triangle to the figure's left): [tex]5\cdot 2=10[/tex]
Thus, the area of the entire figure is:
[tex]8+5+8+10=\boxed{31\:\mathrm{units^2}}[/tex]
