Question

A smaller square of side length 17 feet is cut out of a square board. What is the approximate area (shaded region) of the remaining board in square feet?

Answer 1

The area of the remaining board is (x² - 289) sq. ft.

Explanation:

Let the sides of the bigger square board be, x feet.

It is provided that a smaller square of side length 17 feet is cut out of the bigger square board.

The area of a square is:

`Area=(side)^(2)`

Compute the area of the bigger square board as follows:

`A_(b)=(side_(b))^(2)=x^(2)`

Compute the area of the smaller square board as follows:

`A_(s)=(side_(s))^(2)=(17)^(2)=289`

Compute the area of the remaining board in square feet as follows:

`\text{Remaining Area}=A_(b)-A_(s)`

`=[x^(2)-289]\ \text{square ft.}`

Thus, the area of the remaining board is (x² - 289) sq. ft.