Decompose and Conquer: Finding Area of Irregular Shapes

Mathematics Grades 7th Grade 5:15 Video
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Lesson Description

Learn how to find the area of irregular shapes by breaking them down into smaller, recognizable shapes like rectangles and triangles. This lesson uses the Khan Academy video to guide you through the process.

Video Resource

Finding area by breaking up the shape | Geometry | 6th grade | Khan Academy

Khan Academy

Duration: 5:15
Watch on YouTube

Key Concepts

  • Decomposition of irregular shapes
  • Area of rectangles and triangles
  • Summing areas to find total area

Learning Objectives

  • Students will be able to decompose irregular shapes into rectangles and triangles.
  • Students will be able to calculate the area of rectangles and triangles.
  • Students will be able to find the total area of an irregular shape by summing the areas of its component shapes.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the formulas for the area of a rectangle (Area = length x width) and a triangle (Area = 1/2 x base x height). Discuss how some shapes aren't simple rectangles or triangles, but we can break them apart to find their area.
  • Video Viewing (15 mins)
    Watch the Khan Academy video: 'Finding area by breaking up the shape | Geometry | 6th grade | Khan Academy'. Encourage students to take notes on the steps the presenter uses to solve the problem.
  • Guided Practice (15 mins)
    Work through a similar example problem on the board, guiding students through each step. Emphasize identifying the component rectangles and triangles, finding their individual areas, and summing the areas.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing several irregular shapes. Have them independently find the area of each shape by decomposing it into rectangles and triangles.
  • Wrap-up (5 mins)
    Review the key steps for finding the area of irregular shapes. Address any remaining questions or misconceptions.

Interactive Exercises

  • Shape Decomposition Challenge
    Present students with a complex irregular shape. Have them work in small groups to find multiple ways to decompose the shape into rectangles and triangles. Compare the different approaches and discuss which methods are most efficient.

Discussion Questions

  • Why is it helpful to break down irregular shapes into smaller, recognizable shapes?
  • What are some strategies for deciding how to best decompose an irregular shape?
  • How does knowing the area formulas for rectangles and triangles help us find the area of more complex shapes?

Skills Developed

  • Problem-solving
  • Spatial reasoning
  • Geometric calculation

Multiple Choice Questions

Question 1:

What is the first step in finding the area of an irregular shape?

Correct Answer: Decompose the shape into smaller, regular shapes

Question 2:

Which of these shapes is easiest to calculate the area of?

Correct Answer: Triangle

Question 3:

The area of a rectangle is found by:

Correct Answer: Multiplying length by width

Question 4:

The area of a triangle is found by:

Correct Answer: 1/2 x base x height

Question 5:

If a shape is decomposed into a rectangle with area 20 square units and a triangle with area 10 square units, what is the total area of the original shape?

Correct Answer: 30 square units

Question 6:

Which of the following is NOT a shape you would typically decompose an irregular shape into to find the area?

Correct Answer: Circle

Question 7:

What unit is area commonly expressed in?

Correct Answer: Square meters

Question 8:

Why is it important to use the same units of measurement when finding the area of a shape?

Correct Answer: To get the correct answer

Question 9:

A right triangle has a base of 4 cm and a height of 6 cm. What is the area?

Correct Answer: 12 cm²

Question 10:

A rectangle has a length of 8 meters and a width of 5 meters. What is the area?

Correct Answer: 40 m²

Fill in the Blank Questions

Question 1:

To find the area of an irregular shape, you can __________ it into smaller shapes.

Correct Answer: decompose

Question 2:

The area of a __________ is calculated by multiplying its length and width.

Correct Answer: rectangle

Question 3:

The area of a __________ is calculated by multiplying one-half, the base, and the height.

Correct Answer: triangle

Question 4:

After finding the areas of the smaller shapes, you __________ them together to find the total area.

Correct Answer: add

Question 5:

The unit of measurement for area is always __________.

Correct Answer: squared

Question 6:

A square is a special type of __________ where all sides are equal.

Correct Answer: rectangle

Question 7:

The height of a triangle is always __________ to its base.

Correct Answer: perpendicular

Question 8:

If you decompose a complex shape into a square and a triangle, you need to find the area of each __________ separately before adding them.

Correct Answer: shape

Question 9:

Before calculating the area, make sure all measurements are in the same __________.

Correct Answer: units

Question 10:

The Khan Academy video teaches you how to find area by __________ up the shape.

Correct Answer: breaking

Educational Standards

7.GM.2:Use mathematical models and problems to calculate and justify the area of trapezoids and the area and perimeter of composite figures with rational measurements. 7.GM.2.2:Find the area and perimeter of composite figures. 7.N.2.5:Model and solve problems using rational numbers involving addition, subtraction, multiplication, division, and positive integer exponents.

Teaching Materials

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