Area of Triangles: Unlocking the Formula

Mathematics Grades 7th Grade 1:30 Video
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Lesson Description

Learn how to calculate the area of a triangle using the formula 1/2 * base * height. This lesson explores identifying the base and height and applying the formula to solve for the area.

Video Resource

Example finding area of triangle

Khan Academy

Duration: 1:30
Watch on YouTube

Key Concepts

  • Area of a triangle
  • Base of a triangle
  • Height of a triangle
  • Formula: Area = 1/2 * base * height

Learning Objectives

  • Students will be able to identify the base and height of a triangle.
  • Students will be able to apply the formula Area = 1/2 * base * height to calculate the area of a triangle.
  • Students will be able to solve problems involving the area of triangles.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of area and how it's measured in square units. Briefly discuss the area of rectangles and parallelograms as a bridge to understanding triangles.
  • Video Viewing and Discussion (10 mins)
    Watch the Khan Academy video "Example finding area of triangle". Pause at key points to ask questions and ensure understanding. Focus on how the base and height are identified and how they're used in the formula.
  • Guided Practice (15 mins)
    Work through several examples together as a class. Vary the orientation of the triangles to challenge students' understanding of base and height. Provide scaffolding as needed.
  • Independent Practice (15 mins)
    Students work individually on a set of practice problems. Circulate to provide support and answer questions.
  • Wrap-up and Assessment (5 mins)
    Review the key concepts and address any remaining questions. Administer a quick exit ticket or formative assessment to gauge student understanding.

Interactive Exercises

  • Triangle Area Game
    Use an online interactive game where students can manipulate the base and height of a triangle and see how it affects the area.
  • Real-World Application
    Present a real-world scenario, such as calculating the amount of fabric needed to make a triangular flag, requiring students to apply the area formula.

Discussion Questions

  • What is the difference between the base and the height of a triangle?
  • Why do we multiply by 1/2 when calculating the area of a triangle?
  • How does the orientation of the triangle affect your ability to identify the base and height?

Skills Developed

  • Problem-solving
  • Critical thinking
  • Spatial reasoning
  • Application of formulas

Multiple Choice Questions

Question 1:

What is the formula for the area of a triangle?

Correct Answer: 1/2 * base * height

Question 2:

If a triangle has a base of 10 cm and a height of 5 cm, what is its area?

Correct Answer: 25 cm²

Question 3:

The height of a triangle is always _____ to the base.

Correct Answer: perpendicular

Question 4:

A triangle has an area of 30 square inches and a base of 12 inches. What is its height?

Correct Answer: 5 inches

Question 5:

Which of the following is NOT needed to find the area of a triangle?

Correct Answer: Hypotenuse

Question 6:

The area of a triangle is measured in what units?

Correct Answer: cm²

Question 7:

A right triangle has legs of 3 and 4. What is the area of the triangle?

Correct Answer: 6

Question 8:

What is another way to write 1/2 in decimal form?

Correct Answer: 0.5

Question 9:

If the height is doubled and the base remains the same, what happens to the area of the triangle?

Correct Answer: It doubles

Question 10:

A triangle's base is 8cm and it's area is 20cm². What is the triangles height?

Correct Answer: 5 cm

Fill in the Blank Questions

Question 1:

The area of a triangle is equal to one-half times the base times the ____.

Correct Answer: height

Question 2:

If the base of a triangle is 7 and the height is 4, the area is ____.

Correct Answer: 14

Question 3:

The height of a triangle is always _____ to the base.

Correct Answer: perpendicular

Question 4:

Area is measured in _____ units.

Correct Answer: square

Question 5:

1/2 can also be written as the decimal _____.

Correct Answer: 0.5

Question 6:

The _____ is the bottom side of the triangle (usually).

Correct Answer: base

Question 7:

The triangle area formula is area = 1/2 * _____ * height.

Correct Answer: base

Question 8:

If a triangles height is 10cm and base is 6cm, the area is _____ cm².

Correct Answer: 30

Question 9:

A flat figure that has area is called a 2-_____ figure.

Correct Answer: dimensional

Question 10:

If a triangles area is 12cm² and base is 6cm, the height is _____ cm.

Correct Answer: 4

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.N.2.5:Model and solve problems using rational numbers involving addition, subtraction, multiplication, division, and positive integer exponents. 7.A.4:Use order of operations and properties of operations to generate and evaluate equivalent numerical and algebraic expressions.

Teaching Materials

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