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Clarifications: Each clarification provides an explanation of the indicator/objective to help teachers better understand the concept. Classroom examples are often included to further illustrate the concept. While classroom examples could be shared with the students, the intended audience for the explanation/clarification is the classroom teacher-not the student. In addition, classroom examples may or may not reflect the assessment limits.

Standard 3.0 Knowledge of Measurement

Topic C. Applications in Measurement

Indicator 1. Estimate and apply measurement formulas

Objective c. Estimate and determine the area of a composite figure

  • Use composite figures with no more than four polygons (triangles or rectangles) and whole number dimensions (0 – 500)

Clarification

A composite figure is a geometric shape made up of more than one polygon or plane figure. Typically, any line segments shared by the polygons in a composite figure are not drawn. In figure ABCDE below, line segment DF is shared by rectangle ABCF and triangle FDE and therefore is not drawn. Students should have opportunities to compose and decompose geometric figures by manipulating polygons (rectangles and triangles). The more that students work on seeing the individual polygons that make up composite figures, the better they will understand how to determine their areas.

geometric image

Classroom Example 1

This figure is a rectangle and a triangle combined together. So the area is:

A = lw + 1/2bh
= (10)(5) + 1/2(6)
= 50 + 18
= 68

The area of the figure is 68 square feet.

Classroom Example 2

geometric image

Classroom Example 3

One way to help students see the pieces that make up composite figures is a great puzzle called tangrams. The puzzle consists of seven tangram pieces — a square, 5 triangles, and a parallelogram. The tangram is shown below. One goal of the puzzle is to recreate composite figures like everyday common objects and animals using all seven pieces. This teaches students to look for polygons in a composite figure. Once they see how the pieces are related by shape and size, finding the area of a composite figure will be simpler for them.

geometric image

When you look at the tangram, these are the different pieces that make up the puzzle.

geometric images

In each puzzle there are two parts 1 and 2 and one each of parts 3, 4, and 5.

  • Suppose we let part 2 have an area of 1 sq. unit. Determine the area of each of the other pieces.

    Answer: Part 1 has an area of 4 sq. units, part 3 has an area of 2 sq. units, part 4 has an area of 2 sq. units and part 5 has an area of 2 sq. units.

  • If part 2 has an area of 4 sq. units, what is the area of the original puzzle with all seven pieces?

    Answer: 16 sq. units

Suggested resource: The Fun with Tangrams Kit, Susan Johnston, Dover Publications.
/instruction/clarification/mathematics/grade6/xml/3C1c.xml
Resources for Objective 3.C.1.c:
CLARIFICATIONS | Lesson Seeds | Thinking Skills | Sample Assessments | Public Release Items |