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Understanding the Areas of Parallelograms and Triangles

This chapter covers the essential concepts of calculating the areas of parallelograms and triangles. It introduces key terminology, such as base and height, and presents theorems for determining areas: the area of a rectangle, parallelogram, and triangle. The chapter includes step-by-step instructions on finding the area of these shapes and examples of how to solve for missing dimensions. By mastering these concepts, learners will build a strong foundation in geometry, essential for future mathematical applications.

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Understanding the Areas of Parallelograms and Triangles

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  1. Chapter 10:Area Section 10-1: Area of Parallelograms and Triangles

  2. Objectives: • To find the area of a parallelogram. • To find the area of a triangle.

  3. Vocabulary • Base of a Parallelogram • Altitude of a Parallelogram • Height of a Parallelogram • Base of a Triangle • Height of a Triangle

  4. Theorem 10-1:“Area of a Rectangle” • The area of a rectangle is the product of its base and its height. A = bh height base

  5. Theorem 10-2:“Area of a Parallelogram” • The area of a parallelogram is the product of its base and its height. A = bh height base

  6. Parts of a Parallelogram • A base of a parallelogram is any of its sides. • The corresponding altitude is a segment perpendicular to the line containing that base, drawn from the side opposite that base. • The height is the length of the altitude.

  7. Parts of a Parallelogram (continued)

  8. Finding the Area of a Parallelogram • Find the area of the parallelogram:

  9. Finding the Area of a Parallelogram • Find the area of the parallelogram:

  10. Finding a Missing Dimension • Find the value of x. x 3 4 8

  11. Theorem 10-3:“Area of a Triangle” • The area of a triangle is half the product of the base and the corresponding height.

  12. Parts of a Triangle • A base of a triangle is any of its sides. • The corresponding height is the length of the altitude to the base.

  13. Finding the Area of a Triangle • Find the area of the triangle: 9 16

  14. Finding the Area of a Triangle • Find the area of the triangle: 5 6

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