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Understanding Volume and Area of Composite Shapes and Prisms

This lesson explores the concepts of area and volume, focusing on composite shapes and different types of prisms. Students will calculate the area of given shapes and find the volume using the appropriate formulas. The lesson covers rectangular and triangular prisms, highlighting the relationship between base area and height in volume calculations. Examples include finding the volume of various prisms using dimensions provided, as well as a comparison task involving volumes of boxed games. The aim is to enhance students' spatial reasoning and measurement skills.

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Understanding Volume and Area of Composite Shapes and Prisms

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  1. Opening Activity 1. What is the area of the composite shape below: 1.5 ft 2 ft 2. Find the area of the blue shaded section below: 11 ft 6 ft 4 ft

  2. Chapter 8 Lesson 4 Volume of Prisms

  3. Objective: Students will find the volume of prisms.

  4. The volume of a rectangular prism is the product of the length l, the width w, and the height h. It is also the are of the base B times the height. h w l B=lw V=lw or V=Bh The volume of a three-dimensional figure is the measure of space it occupies. It is measured in cubic units such as cubic centimeters or cubic inches.

  5. Example 1: Find the volume of the rectangular prism. 3m 5m 9.5m Volume formula for a rectangular prism: V=lwh V=(9.5)(5)(3)

  6. The volume V of a triangular prism is the area of the base B times the height h. V= Bh Remember: The base is a triangle so the area of the base B is: Note: In the volume equation, do not confuse the height of the triangle in the base with the height of the prism

  7. Example 2: Find the volume of the triangular prism. 7in 5 in 4in V=Bh Where B is the area of the triangle: Take the area of the triangle base times the height of the prism.

  8. Example 3: Find the volume of the triangular prism. 9m 10m 7m Find the area of the triangle base then multiply by the height of the prism.

  9. Example 4: The game Planet Bugs comes in the box shown below. The game Fire and Ice comes in a box that is also shown below. Which game box has the greater volume? 4 in 4.5 in 5 in 6 in 9 in 8.5 in Planet Bugs Fire and Ice V=lwh V=lwh V=(8.5)(6)(4) V=(9)(5)(4.5) The Planet Bugs box has the greater volume with 204 cubic inches.

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