Lesson 3

Lots of Rectangles

  • Let’s express the areas of some rectangles.

3.1: Math Talk: Many Ways to Area

A rectangle is partitioned into smaller rectangles. Explain why each of these expressions represents the area of the entire rectangle.

rectangle partitioned into smaller rectangles. width of all = 7 units. lengths from left to right = 7, 7, 4, and 4 units.

\(7(7+7+4+4)\)

\(7(2 \boldcdot 7 + 2 \boldcdot 4)\)

\(7^2+7^2+4 \boldcdot 7+4 \boldcdot 7\)

\(2(7^2) + 2 (4 \boldcdot 7)\)

3.2: Representing Areas

Figures A through F.


Match each figure with one or more expressions for its area. Every shape that looks like a square is a square.

  • \(2 \boldcdot 3^2\)
  • \(6n^2\)
  • \(n^2+1^2\)
  • \(3^2\)
  • \((n+1)(n+1)\)
  • \((2n)(3n)\)
  • \((n+1)^2\)
  • \(3(3+3)\)
  • \(n^2\)
  • \((n+n)(n+n+n)\)
  • \(3^2+3^2\)

3.3: Areas of Rectangles

Complete the table with the length, width, and area of each rectangle.

Figures A through E.
rectangle length (units) width (units) area (square units)
A \(a+4\)
B 2
C
D
E

Summary