Answer:
Step-by-step explanation:
1. Rectangle + Semi-Circle
[tex]A = a*b + \frac{\pi r^{2}}{2}\\a=6, b=4, r=\frac{a}{2} = 3\\A = 24 + 4.5 \pi = 38.14 in^{2}\\[/tex]
2. Large Rectangle - Small Rectangle
[tex]A = 15 * 5 - 6*3 = 75 - 18 = 57 in^{2}\\[/tex]
3. Rectangle - Trapezoid
[tex]A = a * b - \frac{c+d}{2}h = 20*17 - 6 * \frac{6+12}{2} = 340 - 54 = 286 cm^{2}\\[/tex]
4. The composite figure is a rectangle if the triangle is moved to left and fills the missing part
[tex]A = a * b = 10 * 9 = 90 m^{2}\\[/tex]
5. Square - Triangle
A = [tex]A = a^{2} - \frac{b^{2}}{2} = 8 * 8 - \frac{4 * 4}{2} = 64 - 8 = 56 cm^{2}\\[/tex]
6. Circle - Square
[tex]A = \pi r^{2} - a^{2} = 64 \pi - 12 * 12 = 64 \pi - 144 = 57.06 m^{2}[/tex]
7. Square - Triangle
[tex]A = a^{2} - \frac{b*h}{2} = 15 * 15 - \frac{10 * 8}{2} = 225 - 40 = 185 sq.ft.[/tex]
8. Rectangle + Triangle
[tex]A = a *b + \frac{a*h}{2} = 9.5 * 9 + \frac{9.5*12}{2} = 85.5 + 57 = 142.5 in^{2}\\[/tex]
9. Triangle + Rectangle
[tex]A = \frac{a*b}{2} + c * d = \frac{12*10}{2} + 12 * 6 = 60 + 72 = 132 sq.ft.[/tex]
10. Rectangle + Quarter Circle
[tex]A = r * b + \frac{\pi r^{2}}{4} = 6 * 8 + \frac{36 \pi}{4} = 48 + 9 \pi = 76.27 in^{2}\\[/tex]
11. Square + Rectangle
[tex]A = a^{2} + b * c = 7 * 7 + 9 * 14 = 49 + 126 = 175 m^{2}[/tex]
12. Rectangle - 2 * Square
[tex]A = a * b - 2 * c^{2} = 25 * 18 - 2 * 8 * 8 = 450 - 128 = 322 sq.ft.[/tex]
13. Trapezoid
[tex]A = \frac{a+b}{2} * h = \frac{10+15}{2} * 15 = 12.5 * 15 = 187.5 sq.ft.[/tex]
14. Trapezoid - Rectangle
[tex]A = a * h - c * d = 12 * 7 - 9 * 5 = 84 - 45 = 39 in^{2}[/tex]
15. Rectangle - Triangle
[tex]A = a * b - \frac{a * b}{2} = \frac{a*b}{2} = \frac{10 * 20}{2} = 100 in^{2}[/tex]
16. Square + Trapezoid
[tex]A = a^{2} + \frac{a + b}{2} * h = 25 + \frac{5 + 9.5}{2} * 6 = 25 + 43.5 = 68.5 in^{2}[/tex]
