Answer:
130.5ft²
Step-by-step explanation:
Hello There!
The figure shown is a composite figure ( so we can't find the area of it using one formula )
That being said we want to break the irregular figure into regular figures in which the area can simply be found using a formula
The figure would be broken in to the following shapes
A rectangle with a width of 4 ft and a length of 9 ft
A rectangle with a width of 8 ft and a length of 9 ft
A triangle with a height of 5 ft and a base of 9 ft
Now that we have broken the irregular figure into regular shapes we want to find the area of each individual shape
For the smaller rectangle:
The area of a rectangle can simply be calculated by multiplying the width and length
So A = 9 * 4
9 * 4 = 36
so the area of the smaller rectangle is 36ft²
For the larger rectangle
Once again the area can simply be found by multiplying the width and length
A = 8 * 9
8 * 9 = 72
so the area of the larger rectangle is 72ft²
For the triangle
To find the area of a triangle we want to use this formula
[tex]A = \frac{bh}{2}[/tex]
where b = base and h = height
We have already identified the base and height so all we have to do is plug in the values into the formula
[tex]A=\frac{5*9}{2} \\5*9=45\\\frac{45}{2} =22.5[/tex]
so the area of the triangle is 22.5ft²
Finally we add the areas of each regular figure
22.5 + 72 + 36 = 130.5
so we can conclude that the area of the composite figure is 130.5ft²
