Question

Hint # 1- Subtract the area of the small rectangle and the area of the triangle from the area of the large rectangle.

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Answer 1

29ft^2

Explanation:

The cut out parts

rectangle
`A=lw=4*2=8ft^2`

triangle
`A=(ab)/(2) =(2*2)/(2) =2ft^2`

Shaded area

smallest rectangle

`A=lw=3*1=3ft^2`

Middle rectangle

`A=lw=5*2=10ft^2`

Biggest rectangle

`A=lw=7*2=14ft^2`

Shaded triangle equal

`A=(ab)/(2) =(2*2)/(2) =2ft^2`

`A_(t)=3+10+14+2=29ft^2`

hope this helps :)

Answer 2

29 ft^2

Explanation:

Let us create a rectangle around this figure, having apparent dimensions 5 by 7 feet. We can conclude the area of the figure by subtracting the non - shaded region from the area of this rectangle;

Area of rectangle ⇒ 5 * 7 = 35 ft^2

Now the non - shaded region can be represented though a triangle, and a rectangle, the triangle having dimensions 2 feet by 2 feet, the rectangle with dimensions 4 feet by 1 foot;

Area of triangle ⇒ 1/2 * base * height = 1/2 * 2 * 2 = 2 ft^2,

Area of mini rectangle ⇒ length * width = 4 * 1 = 4 ft^2

By the Partition Postulate, the area of the shaded region is, consecutively; 35 - 2 - 4 = 29 square feet

Answer: 29 ft^2