Analyzing The Formula of A Parallelogram & Trapezoid

Analyzing The Formula of A Parallelogram & Trapezoid

Introduction to Parallelograms

Opening

Introduction to Parallelograms

A parallelogram is a quadrilateral that has two pairs of parallel sides.

The base of a parallelogram can be any side.

The height is the perpendicular distance from the base to the opposite side.

  • Watch the video.
  • Using what you know about the area of a rectangle, make a prediction about the formula for the area of a parallelogram.

VIDEO: Area of a Parallelogram

Introduction to Trapezoids

Opening

Introduction to Trapezoids

A trapezoid is a quadrilateral with exactly one pair of parallel sides.

The bases of a trapezoid are the parallel sides.

The height is the perpendicular distance between the bases.

  • Watch the video.
  • Using what you know about the area of a parallelogram, determine the formula for the area of a trapezoid.

VIDEO: Area of a Trapezoid

Math Mission

Opening

Explore the formula for the area of a parallelogram and the area of a trapezoid.

Areas of Parallelograms

Work Time

Areas of Parallelograms

The formula for the area of a parallelogram is:
area = base • height, or A = bh

Use the Parallelogram interactive to explore the area of a parallelogram. Move the vertices of the parallelogram and explore what happens to the area.

  • What happens if you keep the height constant and change the base?
  • What happens if you keep the base constant and change the height?
  • What happens if you keep the height and base constant and change one of the angles?

INTERACTIVE: Parallelogram

Hint:

To increase the height, move the top side farther away from the base.

Areas of Trapezoids

Work Time

Areas of Trapezoids

The formula for the area of a trapezoid is:
area = 12(base 1 + base 2) • height, or A = 12(b1 + b2)h

Use the Trapezoid interactive to explore the area of a trapezoid. Move the vertices of the trapezoid and explore what happens to the area.

  • What happens if you keep the height constant and change one of the bases?
  • What happens if you keep the bases constant and change the height?
  • What happens if you keep the height and bases constant and change one of the angles?

INTERACTIVE: Trapezoid

Prepare a Presentation

Work Time

Prepare a Presentation

  • Select one of your conclusions about what happens to the area of a parallelogram or a trapezoid when you change one or more variables.
  • Be prepared to demonstrate your conclusion using the Parallelogram or Trapezoid interactive, and to support your thinking mathematically.

Challenge Problem

Suppose you start with a parallelogram and then slide a pair of opposite sides in opposite directions along parallel lines.

  • Predict how the area will change. Use the Parallelogram interactive to test your prediction.
  • Support your prediction with data from the Parallelogram interactive.

INTERACTIVE: Parallelogram

Make Connections

Performance Task

Ways of Thinking: Make Connections

  • Take notes about classmates’ conclusions concerning what happens to the area of a parallelogram or a trapezoid when you change one or more variables.

Hint:

As your classmates present, ask questions such as:

  • What surprised you in your exploration of parallelograms?
  • What surprised you in your exploration of trapezoids?
  • How does your exploration of parallelograms compare to your exploration of trapezoids? What is the same and what is different?

Area of Parallelograms and Trapezoids

Formative Assessment

Summary of the Math: Area of Parallelograms and Trapezoids

  • Write a summary of what you learned about the area of parallelograms and trapezoids.

Hint:

Check your summary:

  • Do you provide the area formulas for a parallelogram and a trapezoid with explanations of what each variable represents?
  • Area of a parallelogram = bh
  • Area of a parallelogram = h(b1+b2)2
  • Do you include sketches or written descriptions showing how you found the formulas?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

One thing that surprised me about the area of parallelograms and trapezoids was …