Answer:
1008 squares
Step-by-step explanation:
You want to know the number of 1-inch squares that would be required to cover the given irregular area.
Figure area
The given figure can be decomposed into a rectangle that is 4 feet long and 2 feet wide, with two triangular cut-outs. The base of each of those triangles is ...
4 ft - (2 ft +1 ft) = 1 ft
and the height is marked as 1 ft
Triangle area
The area of a triangle is given by ...
A = 1/2bh
Each triangle has an area of ...
A = 1/2(1 ft)(1 ft) = 1/2 ft²
There are 2 of them, so their total area is ...
2 × (1/2 ft²) = 1 ft²
Rectangle area
The area of the overall rectangle is ...
A = LW
A = (4 ft)(2 ft) = 8 ft²
Shaded area
The shaded area of the figure is the difference between the rectangle area and the total area of the two triangle cut-outs:
area = 8 ft² - 1 ft² = 7 ft²
Square inches
A foot is 12 inches, so a square foot is ...
A = (12 in)(12 in) = 144 in²
The figure covers 7 square feet, so its total area in square inches is ...
(7 ft²)×(144 in²/ft²) = 1008 in²
You would need 1008 1-inch squares to cover the entire shape.
