By Glenda Lappan, James T. Fey, William M. Fitzgerald, Susan N. Friel, Elizabeth Philips
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In this investigation, you will look for rules for finding the area of triangles using what you know about rectangles. 1 A square centimeter is 1 centimeter by 1 centimeter. It has an area of 1 square centimeter. Sketch a square centimeter such as the one here. 1 cm2 1 cm 1 cm • • • Draw one diagonal to form two triangles. What is the area of each triangle? Is the perimeter of one of the triangles greater than, less than, or equal to 3 centimeters? 1 Finding Area and Perimeter A. On the next page, six triangles labeled A–F are drawn on a centimeter grid.
Like triangles, parallelograms are often described by measures of side length, base, and height. 1 Finding Measures of Parallelograms As you work with parallelograms, remember what you know about triangles and look for ways to relate these two figures. 1 Here are three parallelograms with the base and height of two parallelograms marked. What do you think the base and the height of a parallelogram mean? How do you mark and measure the base and height of the third figure? 1 Finding Measures of Parallelograms Six parallelograms labeled A–F are drawn on the centimeter grid on the next page.
C. Does changing which side you label the base change the area of the triangle? Explain. D. When finding the area of a triangle, are there advantages or disadvantages to choosing a particular base and its corresponding height? Explain. Homework starts on page 44. 3 What’s the Area? Sometimes the word “family” is used to describe relationships among objects. 1 2 3 4 For example, if Tamarr says that 2 , 4 , 6 , and 8 form a “family” of fractions, what might she mean? This problem challenges you to make a triangle “family” on a coordinate grid.