Answer:
[tex]A_{total} = 25\ ft^2[/tex]
Step-by-step explanation:
Step 1: Determine the area of the square
[tex]A = s^2[/tex]
[tex]A = (3\ ft)^2[/tex]
[tex]A = 9\ ft^2[/tex]
Step 2: Split the top figure into a square and triangle
Determine the area of the rectangle
[tex]A = l * w[/tex]
[tex]A = (7\ ft - 3\ ft) * (5\ ft - 2\ ft)[/tex]
[tex]A = (4\ ft) * (3\ ft)[/tex]
[tex]A = 12\ ft^2[/tex]
Determine the area of the triangle
[tex]A = \frac{b * h}{2}[/tex]
[tex]A = \frac{\frac{7\ ft - 3\ ft}{2} * (5\ ft - 3\ ft)}{2}[/tex]
[tex]A=\frac{2\ ft * 2\ ft}{2}[/tex]
[tex]A = \frac{4\ ft^2}{2}[/tex]
[tex]A = 2\ ft^2[/tex]
Since there are two right triangles in the triangle that we have we multiply the area that we got by 2 to get the total area.
[tex]A_{triangle} = 2\ ft^2*2[/tex]
[tex]A_{triangle} = 4\ ft^2[/tex]
Step 3: Determine the total area
[tex]A_{total} = 9\ ft^2 + 12\ ft^2 + 4\ ft^2[/tex]
[tex]A_{total} = 25\ ft^2[/tex]
Answer: [tex]A_{total} = 25\ ft^2[/tex]
