New Unit: Area, Surface Area, and Volume

Topic 1: AREA OF TRIANGLES, QUADRILATERALS, AND POLYGONS

In this topic, students relate the parallelogram to the more familiar rectangle and discover that the areas of

both figures are calculated the same way (area = base × height, or A = bh). Students also discover that a right

triangle is exactly half of a rectangle. From there, students generalize that the area of every triangle is

one-half the area of its corresponding parallelogram. They then generalize the formula for the area of a triangle

as A b = h 1

2 . Using their knowledge of the area formulas for rectangles, triangles, and parallelograms, students

find the areas of irregularly shaped polygons (or composite figures) by composing or decomposing the figures

into familiar shapes and finding their areas.

You can expect to see homework that asks your child to do the following:

▪ Draw and label the altitude, or height, of a parallelogram.

▪ Calculate the areas of rectangles, parallelograms, and triangles using the area formula for each figure.

▪ Compare the areas of two different figures to see whether they are the same.

▪ Through decomposition and composition, calculate the area of a composite figure given the lengths of its

sides.

▪ Use knowledge of area to solve real-world problems