Simplifying and writing expressions 2: area

In this grade 6 or pre-algebra lesson, we continue our study of expressions, this time writing and simplifying expressions for the area of rectangles. This involves multiplying x times x to get x².

For example, the area of a rectangle with sides 4x and 2x becomes 4x(2x) = 8x².

After writing the expression for the area of rectangles when the sides are known, we solve the opposite problem: if the area is given in terms of a variable, how long are the sides? For example, the area of a square is 16s². How long is its side?

Next, we solve a multi-step algebraic word problem: The perimeter of a square is 8x. What is its area? This problem requires us to find the length of side of this square, which is 2x. Then it's easy to find the area by multiplying: 2x(2x) = 4x².

The last problem involves a rectangular area composed of two rectangles. We find both its perimeter and area.

(The first part of this lesson is found here: Simplifying and writing expressions 1: length and perimeter.)

See also

Math Mammoth Expressions and Equations — a short workbook where you can find worksheets that match this lesson.

Math Mammoth Grade 6 Curriculum — again, contains worksheets to match this lesson.

Math Mammoth Grade 7 curriculum (pre-algebra)

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