Triangle Area

Abstract

Students learn about finding the area of a triangle.

Objectives

Upon completion of this lesson, students will:

  • be able to find the area of a right triangle
  • reinforce the idea of area measure
  • understand the formula for finding the area of a right triangle

Standards Addressed

Grade 6

  • Geometry

    • The student solves problems (including real-world situations) using perimeter, area, or volume.

Grade 7

  • Geometry

    • The student solves problems (including real-world situations).

Grade 8

  • Geometry

    • The student solves problems (including real-world situations).

Sixth Grade

  • Geometry

    • Solve real-world and mathematical problems involving area, surface area, and volume.

Number and Quantity

  • Quantities

    • Reason quantitatively and use units to solve problems.

Grades 3-5

  • Measurement

    • Apply appropriate techniques, tools, and formulas to determine measurements

Technical Mathematics I

  • Geometry and Measurement

    • Competency Goal 2: The learner will measure and apply geometric concepts to solve problems.

Technical Mathematics II

  • Geometry and Measurement

    • Competency Goal 1: The learner will use properties of geometric figures to solve problems.

5th Grade

  • Measurement

    • The student will demonstrate through the mathematical processes an understanding of the units and systems of measurement and the application of tools and formulas to determine measurements.

Geometry

  • Geometry

    • Standard G-3: The student will demonstrate through the mathematical processes an understanding of the properties and special segments of triangles and the relationships between and among triangles.

Student Prerequisites

  • Technological: Students must be able to:
    • perform basic mouse manipulations such as point, click and drag
    • use a browser for experimenting with the activities

Teacher Preparation

  • access to a browser
  • construction paper and pencil
  • rulers
  • grid paper

Key Terms

area

The number of square units needed to cover a surface

right angle

An angle of 90 degrees

right triangle

A triangle containing an angle of 90 degrees

Lesson Outline

  1. Focus and Review

    • Review any pertinent vocabulary such as area and square unit.
    • Remind students about area of a rectangle and ask them to recall how to find the area of such a shape. If students answer "length times width" ask them to explain why that formula works.

  2. Objectives

    • Ask the students to think about the area formula and if it works for shapes other than rectangles. Tell them that today we will be looking to find the area of a different shape - a right triangle.

  3. Teacher Input

    • Ask students to recall what they have learned about measuring area so far. Illicit from them:
      • area is measured in square units such as cm sq, in sq, ft sq, etc.
      • an explanation of what area means

  4. Guided Practice

    • Have all the students cut out a square. Do not specify the size. (You may want to remind the students that the corners of a square are right angles.)
    • Once the students have completed their squares, have them measure the area of their square.
    • Have the students crease their square from the lower left corner to the upper right corner and cut along the crease to create two right triangles with equal areas.
    • Ask the students if anyone can tell the class the area of one or both of the triangles.
    • Have that student explain to the class how he/she knew the area of the triangle.
    • Ask the class to come up with a formula to calculate the area of right triangles.
    • Tell them that they need to be able to explain why their equation should work for all right triangles.
    • If no one mentions the length * width / 2 method, mention the method to the class and have them try it.
    • Show the students how to operate the Triangle Explorer Applet.

  5. Independent Practice

    • Have the students work in pairs to explore the Triangle Explorer Applet.
    • Instruct the students to work 5 easy problems, 5 medium problems, and 5 hard problems.
    • Have the students draw several of the computer generated shapes on a sheet of graph paper and write the areas beside the shapes. This helps the students to process what they are doing on screen.

  6. Closure

    • Clarify how to calculate the area of a right triangle and ask if there are any questions.
    • Discuss the different ways the students used to calculate the areas of more difficult triangles.