Answer:
[tex] \displaystyle d) 36 \: {in}^{2} [/tex]
Step-by-step explanation:
the polygon can be separated in two parts
- rectangle
- triangle
let's figure out the area of the rectangle
recall that,
- [tex] \displaystyle A_{ \rm rect} =l \times w[/tex]
given that,
thus substitute:
- [tex] \displaystyle A_{ \rm rect} =9\times 3[/tex]
simplify multiplication:
- [tex] \displaystyle A_{ \rm rect} =27[/tex]
let's figure out the area of the triangle
remember that,
[tex] \displaystyle A_{ \rm triangle} = \frac{1}{2} \times b\times h[/tex]
substitute the value of b and h:
[tex] \displaystyle A_{ \rm triangle} = \frac{1}{2} \times 9\times 2[/tex]
reduce fraction:
[tex] \displaystyle A_{ \rm triangle} = 9[/tex]
now the area of the polygon would be the total area of the rectangle and triangle thus
[tex] \displaystyle A_{ \rm polygon} = 27 + 9[/tex]
simplify addition:
[tex] \displaystyle A_{ \rm polygon} = 36[/tex]
hence our answer is D)
