# Discovering the Area Formula for Trapezoids

Lesson 3 of 4

6th grade

45–60 minutes

**Description**

Students explore several strategies for calculating the area of a trapezoid while discovering the area formula for trapezoids.

**Materials**

### Introduce

This lesson is written to focus on **trapezoids** that have exactly one pair of parallel sides. It may be necessary to review the properties of **trapezoids **in relation to other **quadrilaterals**.

In partners or small groups display or distribute the **Trapezoid** or Not? Activity Sheet (download from Materials section above), and ask students to identify which **quadrilaterals** are **trapezoids**. Discuss responses to address any misconceptions.

### Explore

The main portion of this lesson involves the derivation of an area formula for trapezoids.

Divide students into partners or small groups and distribute the **Area** of **Trapezoids** Activity Sheet. Have students work together to come up with multiple strategies for determining the **area** of a **trapezoid**, using a different strategy for each **trapezoid**.

After students have had some time to discuss suggestions in their groups, conduct a whole class discussion.

The discussion should start with asking students for their ideas about decomposing the **trapezoid**. Once all ideas have been discussed, the teacher can encourage students to find additional representations by asking guiding questions to suggest alternative strategies.

### Synthesize

After highlighting a variety of strategies to discover the **area** of a **trapezoid**, be sure to emphasize that all strategies result in the same formula.

### Assessment (optional)

Students work together to measure the **bases **and heights and calculate the **area** of the **trapezoids** on the **Trapezoid** Activity Sheet.

### Extension

**Activity 1 (Technology Option)**

Open the **Area Tool** using a computer. The **trapezoids** tab can be used to demonstrate that the midline is the average of the two **bases** as well as investigating the relationship of the height and the length of the **bases** to the **area**.

**Activity 2**

The state of Nevada is relatively close to the shape of a **trapezoid**. Find the approximate **area** of the state using the border lengths of the surrounding states. The distance along the Utah border is approximately 554 km, the distance along the Oregon/Idaho border is about 487 km, the distance along the California border is about 330 km on the west side of Nevada and about 635km on the southwest side; the distance on the Arizona border is about 218 km. Using what you know about **trapezoids**, estimate the **area** of Nevada. Justify your answer, and provide an explanation of the mathematics used.

### Teacher Reflection

- Which strategy allowed students to visualize the formula for finding the
**area **of a **trapezoid**?
- Which strategy do you think resonated with students the most? Why?
- What misconceptions did your students have and how were they addressed?
- How did the questions you posed strengthen student understanding?

Leave your thoughts in the comments below.