**High School Number Sense Lesson 39: Squares**

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:**

**P = 4L**

A = L

A = D

A = L

^{2}A = D

^{2}/2**Example 1: What is the side length of a square with area 361?**

- 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.

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 ___

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**.

**Here's a free worksheet to help you practice Squares:**

squares.pdf |

**Up Next for High School: Rhombus**