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