**High School Number Sense Lesson 40: Rhombuses (Rhombi)**

A rhombus is a 4-sided polygon whose sides all have the

**same length**. As such, a rhombus is often called an

**equilateral quadrilateral**, a

**diamond**, or a

**kite**. By definition, a square is also a rhombus (but not all rhombi are squares).

Questions about rhombi appeared

**3 times**this year, with the median placement at

**question # 39**.

**Number Dojo Level: 162**

There are 3 formulas that need to be learned for rhombi; the third is by far the most often-tested:

**P = 4L**(the perimeter is equal to 4 times the length of a side)

2.

**A = BH**(the area is equal to the length of the base times the height)

3.

**A = D**(the area is 1/2 the product of the lengths of the two diagonals)

_{1}D_{2}/2

Example 1: If the perimeter of a rhombus is 14 in, then one side measures ___ in

Example 1: If the perimeter of a rhombus is 14 in, then one side measures ___ in

- Divide the perimeter by 4 to find the length of one side. 14 ÷ 4 =
**3.5**.

**Example 2: Find the area of a rhombus with base 12 and height 7.**

- A = BH = 12 x 7 =
**84**.

**Example 3: The area of a rhombus with diagonals 4 and 5 is ___**

- Multiply the diagonals. 4 x 5 =
**20**. - Divide the product by 2. 20 ÷ 2 =
**10**.

**Example 4: The diagonals of a rhombus are 22" and 30". The area is ___ square inches.**

- Multiply the diagonals. 22 x 30 =
**660**. - Divide the product by 2. 660 ÷ 2 =
**330**.

**Example 5: The diagonals of a rhombus are 2√3 and 4√3. The area of the rhombus is ___**

- Multiply the diagonals. 2√3 x 4√3 = 8(√3 x √3) = 8(3) =
**24**. - Divide the product by 2. 24 ÷2 =
**12**.

**Example 6: The area of a rhombus is 42. One diagonal is 6, and the other is ___**

- The area is 1/2 the product of the diagonals, so multiply by 2 and then divide by one diagonal to find the other.
- 42 x 2 =
**84**. 84 ÷ 6 =**14**.

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

rhombus.pdf |

**Up Next for High School: MultRoots**