**MIddle School Number Sense Lesson 43: Trapezoids**

Trapezoids are 4-sided polygons (quadrilaterals) with at least one pair of parallel sides, which are called

**bases**. (Imagine a triangle with its top cut off--with a cut parallel to the base). Questions about trapezoids appeared

**6 times**this year, with a median placement at

**question # 43**.

**Number Dojo Level: 161**

There are two concepts that have come up recently on number sense tests--one that may be familiar to you and one that may not be.

First, the

**area**of a trapezoid can be calculated by multiplying its

**height**(or altitude) by the

**average of its bases' lengths**. This can be written as:

**A = H(b + B)/2**

**median**(or midline). This line is the result of drawing a line parallel to, and halfway between, the two bases. The median happens to have a length that is equal to the average of the lengths of the bases. The median can be calculated like this:

**M = (b + B)/2**

**height**by the

**length of its median**. This can be written as:

**A = HM or A = MH**

**Example 1: The area of a trapezoid with bases 12 and 18 and height 8 is ___**

- A = H(b + B)/2 = 8(12 + 18)/2 = 8(30)/2 = 8(15) =
**120**.

**Example 2: The area of a trapezoid with bases 9 and 15 and height 6 is ___**

- A = H(b + B)/2 = 6(9 + 15)/2 = 6(24)/2 = 6(12) =
**72**.

**Example 3: What is the area of a trapezoid with bases 18 and 24 and altitude 11?**

- A = H(b + B)/2 = 11(18 + 24)/2 = 11(42)/2 = 11(21) =
**231**.

**Example 4: The median of a trapezoid with bases 14 and 40 is ___**

- M = (b + B)/2 = (14 + 40)/2 = 54/2 =
**27**.

**Example 5: The area of a trapezoid with median 18 and height 22 is ___**

- A = MH = 18(22) =
**396**.

Example 6: Find the median of a trapezoid if the area is 42 and the height is 10.

Example 6: Find the median of a trapezoid if the area is 42 and the height is 10.

- A = MH, so M = A/H.
- M = 42/10 =
**4.2**

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

trapezoid.pdf |

**Up Next for Middle School: SquareRoot**