Examples with solutions for Area of the Square: True / false

Exercise #1

Look at the square below:

333

Is the perimeter of the square greater than its area?

Video Solution

Step-by-Step Solution

Let's remember that the area of the square is equal to the side of the square raised to the second power.

Also, the perimeter of the square is equal to the side multiplied by 4.

We calculate the area of the square:
A=32=9 A=3^2=9

We calculate the perimeter of the square:

3×4=12 3\times4=12

Therefore, the perimeter is greater than the area of the square.

Answer

Yes

Exercise #2

Look at the square below:

222

Is the perimeter of the square greater than its area?

Video Solution

Step-by-Step Solution

Remember that the area of the square is equal to the side of the square raised to the 2nd power.

Remember that the perimeter of the square is equal to the side of the square multiplied by 4.

We calculate the area of the square:

A=22=4 A=2^2=4

We calculate the perimeter of the square:

2×4=8 2\times4=8

Therefore, the perimeter is greater than the area.

Answer

Yes

Exercise #3

Look at the square below:

4.54.54.5

Is the perimeter of the square greater than the area of the square?

Video Solution

Step-by-Step Solution

Remember that the area of the square is equal to the side of the square raised to the 2nd power.

Remember that the perimeter of the square is equal to the side of the square multiplied by 4.

We calculate the area of the square:

A=4.52=20.25 A=4.5^2=20.25

We calculate the perimeter of the square:

4.5×4=18 4.5\times4=18

Therefore, the perimeter is not greater than the area.

Answer

No

Exercise #4

Look at the square below:

444

Is the perimeter of the square greater than its area?

Video Solution

Step-by-Step Solution

Let's remember that the area of the square is equal to the side of the square raised to the second power.

Let's remember that the perimeter of the square is equal to the side multiplied by 4.

We calculate the area of the square:

A=42=16 A=4^2=16

We calculate the perimeter of the square:

4×4=16 4\times4=16

Therefore, the perimeter is not greater than the area (they are equal).

Answer

False

Exercise #5

Look at the square below:

101010

Is the perimeter of the square greater than its area?

Video Solution

Step-by-Step Solution

Remember that the area of the square is equal to the side of the square raised to the 2nd power.

Remember that the perimeter of the square is equal to the side of the square multiplied by 4.

We calculate the area of the square:

A=102=100 A=10^2=100

We calculate the perimeter of the square:

10×4=40 10\times4=40

Therefore, the perimeter is not greater than the area.

Answer

No

Exercise #6

Look at the square below:

666

Is the perimeter of the square greater than its area?

Video Solution

Step-by-Step Solution

Given that we have one side equal to 6, we can multiply and calculate the area:

62=36 6^2=36

The perimeter can also be calculated:

6×4=24 6\times4=24

From this we can conclude that the area of the square is greater than its perimeter: 36 > 24

Answer

No

Exercise #7

Look at the square below:

999

Is the area of the square greater than the perimeter of the square?

Video Solution

Step-by-Step Solution

Remember that the area of the square is equal to the side of the square raised to the 2nd power.

Remember that the perimeter of the square is equal to the side of the square multiplied by 4.

We calculate the area of the square:

A=92=81 A=9^2=81

We calculate the perimeter of the square:9×4=36 9\times4=36

Therefore, the area is greater than the perimeter.

Answer

Yes

Exercise #8

Look at the square below:

555

Is the perimeter of the square greater than the area of the square?

Video Solution

Step-by-Step Solution

Let's remember that the area of the square is equal to the side of the square raised to the second power.

Keep in mind that the circumference of the square is equal to the side of the square times 2.

Let's remember that the perimeter of the square is equal to the side multiplied by 4.

Calculate the area of the square:

A=52=25 A=5^2=25

Then calculate the perimeter of the square:

5×4=20 5\times4=20

Therefore, the perimeter is not greater than the area.

Answer

No

Exercise #9

Look at the square below:

444

Is the sum of the two diagonals greater than the sum of the 3 sides of the square?

Video Solution

Step-by-Step Solution

Let's look at triangle BCD, let's calculate the diagonal by the Pythagorean theorem:

DC2+BC2=BD2 DC^2+BC^2=BD^2

As we are given one side, we know that the other sides are equal to 4, so we will replace accordingly in the formula:

42+42=BD2 4^2+4^2=BD^2

16+16=BD2 16+16=BD^2

32=BD2 32=BD^2

We extract the root:BD=AC=32 BD=AC=\sqrt{32}

Now we calculate the sum of the diagonals:

2×32=11.31 2\times\sqrt{32}=11.31

Now we calculate the sum of the 3 sides of the square:

4×3=12 4\times3=12

And we reveal that the sum of the two diagonals is less than the sum of the 3 sides of the square.

11.31 < 12

Answer

No

Exercise #10

Look at the following square:

999

Is the sum of the two diagonals greater than the sum of the 3 sides of the square?

Video Solution

Answer

No

Exercise #11

777

Is the sum of the two diagonals in the above square greater than the sum of the 3 sides of the square?

Video Solution

Answer

No

Exercise #12

Look at the square below:

111111

Is the sum of the two diagonals greater than the sum of the 3 sides of the square?

Video Solution

Answer

False

Exercise #13

Look at the square below:

333

Is the sum of the two diagonals greater than the sum of the 3 sides of the square?

Video Solution

Answer

No

Exercise #14

Look at the square below:

666

Is the sum of the two diagonals greater than the sum of the 3 sides of the square?

Video Solution

Answer

No