Square Geometry: Compare Area vs Perimeter of a 9-Unit Square

Question

Look at the square below:

999

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

Video Solution

Solution Steps

00:00 Is the area of the square greater than its perimeter?
00:03 Side length according to the given data
00:07 The perimeter of the square equals the sum of its sides
00:11 Let's substitute appropriate values and solve for the perimeter
00:15 This is the perimeter of the square
00:18 Let's use the formula for calculating the area of a square (side squared)
00:21 Let's substitute appropriate values and solve for the area
00:29 The perimeter of the square is less than its area
00:33 And this is the solution to the question

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