Unlocking the Area of Triangles: A Visual Adventure

Mathematics Grades 7th Grade 5:29 Video
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Lesson Description

Discover the formula for the area of a triangle (1/2 * base * height) through visual proofs and connections to parallelograms. Understand the relationship between these shapes and master area calculations.

Video Resource

Area of triangles intuition | Algebra I | High School Math | Khan Academy

Khan Academy

Duration: 5:29
Watch on YouTube

Key Concepts

  • Area of a rectangle (base x height)
  • Area of a parallelogram (base x height)
  • Area of a triangle (1/2 x base x height)
  • Relationship between triangles and parallelograms
  • The height of a triangle is the perpendicular distance from the base to the opposite vertex.

Learning Objectives

  • Students will be able to explain why the area of a triangle is half the area of a parallelogram with the same base and height.
  • Students will be able to calculate the area of a triangle using the formula: Area = 1/2 * base * height.
  • Students will be able to identify the base and height of various triangles, including obtuse triangles.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the formulas for the area of a rectangle and a parallelogram. Ask students if they remember the formula for the area of a triangle and if they know why it is what it is.
  • Video Viewing (10 mins)
    Play the Khan Academy video 'Area of triangles intuition'. Instruct students to pay close attention to how the triangle is transformed into a parallelogram.
  • Guided Discussion (10 mins)
    After the video, lead a discussion about the key takeaways from the video. Emphasize the visual proof of how two identical triangles form a parallelogram, which leads to the formula for the area of a triangle.
  • Practice Problems (15 mins)
    Provide students with practice problems where they calculate the area of various triangles. Include examples with different orientations and obtuse triangles.
  • Wrap-up and Assessment (10 mins)
    Summarize the main points of the lesson and have students complete a short quiz to assess their understanding. Review any questions students may have before finishing.

Interactive Exercises

  • Triangle Transformation
    Provide students with paper triangles and scissors. Have them cut out two identical triangles and physically manipulate them to form a parallelogram. This reinforces the visual understanding presented in the video.
  • Area Calculation Challenge
    Present students with a variety of triangles (acute, right, obtuse) with different base and height measurements. Have them work individually or in pairs to calculate the area of each triangle.

Discussion Questions

  • How does the video demonstrate the relationship between a triangle and a parallelogram?
  • Why is the area of a triangle half the area of a parallelogram with the same base and height?
  • How do you identify the base and height of an obtuse triangle?
  • Can you explain in your own words why the formula 1/2 * base * height works to find the area of a triangle?

Skills Developed

  • Visual Reasoning
  • Problem Solving
  • Formula Application
  • Spatial Reasoning
  • Critical Thinking

Multiple Choice Questions

Question 1:

The area of a rectangle is found by multiplying the base and the height. What is the area of a triangle?

Correct Answer: 1/2 x Base x Height

Question 2:

If a triangle has a base of 8 cm and a height of 5 cm, what is its area?

Correct Answer: 20 cm²

Question 3:

The height of a triangle is always:

Correct Answer: Perpendicular to the base

Question 4:

Two identical triangles can be joined to form a:

Correct Answer: Parallelogram

Question 5:

In the formula for the area of a triangle, what does 'b' represent?

Correct Answer: Base

Question 6:

If a parallelogram has a base of 10 inches and a height of 6 inches, what is the area of a triangle with the same base and height?

Correct Answer: 30 inches²

Question 7:

What is the area of a triangle with a base of 12 meters and a height of 7 meters?

Correct Answer: 42 meters²

Question 8:

The base of a triangle is 9 feet and the area is 36 feet². What is the height?

Correct Answer: 8 feet

Question 9:

An obtuse triangle has one angle that is:

Correct Answer: Greater than 90 degrees

Question 10:

What happens to the area of a triangle if you double its height, but keep the base the same?

Correct Answer: The area doubles

Fill in the Blank Questions

Question 1:

The area of a triangle is equal to one-half times the _____ times the height.

Correct Answer: base

Question 2:

A parallelogram has the same area as a ______ with the same base and height.

Correct Answer: rectangle

Question 3:

The height of a triangle is the ______ distance from the base to the opposite vertex.

Correct Answer: perpendicular

Question 4:

If a triangle has a base of 6 cm and a height of 4 cm, its area is _____ cm².

Correct Answer: 12

Question 5:

An angle greater than 90 degrees is referred to as an _____ angle.

Correct Answer: obtuse

Question 6:

The area of a parallelogram is base times _____

Correct Answer: height

Question 7:

The area of a triangle is _____ the area of a parallelogram with the same base and height.

Correct Answer: half

Question 8:

The formula for the area of a triangle is A = 1/2 x b x _____

Correct Answer: h

Question 9:

If the area of a triangle is 25 inches² and the base is 10 inches, the height is _____ inches.

Correct Answer: 5

Question 10:

The base and height of a triangle must form a _____ angle.

Correct Answer: right

Educational Standards

7.GM.2.2:Find the area and perimeter of composite figures. 7.GM.2.1:Develop and use the formula to determine the area of a trapezoid. 7.A.4.1:Use properties of operations (associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents.

Teaching Materials

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