Area of the Square: Worded problems

Increasing a specific element by addition of.....or multiplication by.......True / false Express using Applying the formula Calculate The Missing Side based on the formula

Question 1

At the vertices of a square with sides measuring y cm, 4 squares are drawn with lengths of x cm.

What is the area of the shape?

Question 2

In a square-shaped recreation space, they want to paint part of it white so that the shape of the white paint is triangular.

The length of the play area is 6 meters

one box of paint is required for each meter of paint.

How many buckets of paint do you need to paint the triangular area?

Question 3

The length of the side of the square $$ x+1 $$ cm

$$ (x>3) $$

We extend one side by 1 cm and shorten an adjacent side by 1 cm, and we obtain a rectangle.

What is the area of the square?

Question 4

The length of the side of the square $$ x+1 $$ cm

$$ (x>3) $$

We extend one side by 1 cm and shorten an adjacent side by 1 cm, and we obtain a rectangle.

What is the area of the rectangle?

Question 5

The length of the square is equal to $$ x $$ cm

$$ (x>1) $$ We extend one side by 3 cm and shorten an adjacent side by 1 cm and we obtain a rectangle,

What is the length of the side of the given square if it is known that the two areas are equal?

Examples with solutions for Area of the Square: Worded problems

Exercise #1

At the vertices of a square with sides measuring y cm, 4 squares are drawn with lengths of x cm.

What is the area of the shape?

Video Solution

Step-by-Step Solution

We will refer to two separate areas: the area of the square with side y and the total area of the four squares with sides x,

We'll use the formula for the area of a square with side b:

$S=b^2$ and therefore when applying it to the problem, we get that the area of the square with side y in the drawing is:

$S_1=y^2$ Next, we'll calculate the area of the square with side x in the drawing:

$S_2=x^2$ and to get the total area of the four squares in the drawing, we'll multiply this area by 4:

$4S_2=4x^2$ Therefore, the area of the required figure in the problem, which includes the area of the square with side y and the area of the four squares with side x is:

$S_1+4S_2=y^2+4x^2$ Therefore, the correct answer is A.

Answer

$4x^2+y^2$

Exercise #2

In a square-shaped recreation space, they want to paint part of it white so that the shape of the white paint is triangular.

The length of the play area is 6 meters

one box of paint is required for each meter of paint.

How many buckets of paint do you need to paint the triangular area?

Video Solution

Answer

18 paint boxes

Exercise #3

The length of the side of the square $x+1$ cm

$(x>3)$

We extend one side by 1 cm and shorten an adjacent side by 1 cm, and we obtain a rectangle.

What is the area of the square?

Video Solution

Answer

$x^2+2x+1$

Exercise #4

The length of the side of the square $x+1$ cm

$(x>3)$

We extend one side by 1 cm and shorten an adjacent side by 1 cm, and we obtain a rectangle.

What is the area of the rectangle?

Video Solution

Answer

$x^2+2x$

Exercise #5

The length of the square is equal to $x$ cm

$(x>1)$ We extend one side by 3 cm and shorten an adjacent side by 1 cm and we obtain a rectangle,

What is the length of the side of the given square if it is known that the two areas are equal?

Video Solution

Answer

$x=\frac{3}{2}cm$

Question 1

The square below has an area of 36.

$$ x>0 $$

Calculate x.

Question 2

The side length of a square is X cm

$$ (x>3) $$

We extend one side by 3 cm and shorten an adjacent side by 3 cm, and we get a rectangle.

Which shape has a larger area?

Exercise #6

The square below has an area of 36.

$x>0$

Calculate x.

Video Solution

Answer

$x=5$

Exercise #7

The side length of a square is X cm

$(x>3)$

We extend one side by 3 cm and shorten an adjacent side by 3 cm, and we get a rectangle.

Which shape has a larger area?

Video Solution

Answer

The square