Answer:
[tex] \rm\displaystyle A _{ \text{total}} = 322 {km}^{2} [/tex]
Step-by-step explanation:
refer the attachment
we have a triangle,a rectangle and a square
in order to figure out the area of the total figure we need to figure out the area the attached figure first
Triangle:
the triangle has a base of 18 km and a height of 13+6+2=21km
thus,
the area of the triangle is
[tex] \displaystyle \frac{1}{2} \times 18 km\times 21km[/tex]
reduce fraction:
[tex] \displaystyle 9 km\times 21km[/tex]
simplify multiplication:
[tex] \displaystyle 189 km ^{2} [/tex]
Rectangle:
the rectangle has a length of 13km and a width of 4km
thus,
the area of the rectangle is
[tex] \displaystyle 13km \times 4km[/tex]
simplify multiplication:
[tex] \displaystyle {52km}^{2} [/tex]
Square:
the length of every sides of the square is 9km
thus,
the area of the square is
[tex] \displaystyle {(9km)}^{2} [/tex]
simplify square:
[tex] \displaystyle {81km}^{2} [/tex]
Area-total:
[tex] \rm\displaystyle A _{ \text{total}} = A_{ \text{triangle}} + A_{ \text{rectangle}} + A_{ \text{square}}[/tex]
substitute:
[tex] \rm\displaystyle A _{ \text{total}} = 189 {km}^{2} + 52 {km}^{2} + 81 {km}^{2} [/tex]
simplify addition:
[tex] \rm\displaystyle A _{ \text{total}} = 322 {km}^{2} [/tex]
