Number sense tests have many questions related to geometric shapes (polygons) and their properties. The easiest to work with are squares, which we'll cover today. This concept appeared 7 times this year, with a median spot at question # 38.
Number Dojo Level: 144
Most people know that the area (A) of a square is equal to the square if its side's length (L), and that the perimeter (P) of a square is equal to 4 times its side's length. What most people don't know is that a square's area can also be calculated if the length of the diagonal (D) is known.
Formulas to Know:
- The area is the square of the side length, so take the square root of 361. The answer is 19.
Example 2: The area of a square with side length 25 is ___
- The area is the square of the side length, so square 25. The answer is 625.
Example 3: The area of a square is 196. The perimeter is ___
- Take the square root of 196 to find the side length: 14.
- Multiply 14 by 4 to find the perimeter: 56.
Example 4: The perimeter of a square is 60. The area is ___
- Divide the perimeter (60) by 4 to get the side length: 15.
- Square 15 to get the area: 225.
Example 5: Find the area of a square with diagonal 12.
- The area is 1/2 the square of the diagonal. (12 x 12)/2 = 144/2 = 72.
Example 6: The diagonal of a square is 5√2 inches. The area of the square is ___ square inches.
- The area is 1/2 the square of the diagonal. (5√2 x 5√2)/2 = (25√4)/2 = (25 x 2)/2 = 25.
Example 7: When the perimeter of a square increases from 16 to 28, the corresponding increase in area is ___
- Divide the original perimeter (16) by 4 to find the side's length: 4. Square 4 to find the original area: 16.
- Divide the final perimeter (28) by 4 to find the side's length: 7. Square 7 to find the final area: 49.
- Subtract the original area from the final area. 49 - 16 = 33.