3. Rectangle and Square Area

Area tells how much flat surface is covered.

Formulas:

• Rectangle: \(A = l \times w\)
• Square: \(A = s^2\)

Example: a room is 12 ft by 9 ft. Carpet covers area, so \(A = 12 \times 9 = 108\ \text{ft}^2\).

Common mistake: adding the sides instead of multiplying. Adding side lengths gives perimeter clues, not area.

Deepen your understanding
Use this focused guide to turn Rectangle and Square Area into a dependable GED® problem-solving skill.

Learning targets

• Explain rectangle area as rows times columns of unit squares.
• Switch correctly between area and perimeter for the same rectangle.
• Find a missing side by dividing a known area by the other side.

Step-by-step solving routine

1. Label length and width and confirm they use the same unit.
2. Multiply (l\times w), then attach square units.
3. For a square, use (s^2); for a missing rectangle dimension, rearrange to (l=A\div w).
4. Estimate with nearby friendly numbers to make sure the product has a sensible size.

GED® application
A (12\)-ft by (9\)-ft floor contains (12\times9=108) one-square-foot tiles in an ideal grid. Baseboard for that room is a perimeter question, (2(12+9)=42\) ft, which explains why the same diagram can have two very different answers.

Coach check
Sketch a small unit-square grid inside the rectangle whenever multiplying the dimensions feels abstract.

Visual study gallery
Study each diagram before the worked examples. Name what is measured, identify the needed dimensions or relationships, and explain which formula or rule the picture supports.

10 worked examples and problem solving
Use these examples as guided practice before attempting the session MCQs. Each problem is self-contained, including any needed table or context.

Example 1
Problem: A rectangle is \(7\) units long and \(4\) units wide. What is its area?
Answer: \(28\) square units
Solution: Area of a rectangle is length times width: \(7 \times 4 = 28\). The perimeter trap is \(22\). Pro tip: area multiplies two dimensions and uses square units.

Example 2
Problem: A rectangle is \(12\) units long and \(9\) units wide. What is its area?
Answer: \(108\) square units
Solution: Area of a rectangle is length times width: \(12 \times 9 = 108\). The perimeter trap is \(42\). Pro tip: area multiplies two dimensions and uses square units.

Example 3
Problem: A rectangle is \(15\) units long and \(6\) units wide. What is its area?
Answer: \(90\) square units
Solution: Area of a rectangle is length times width: \(15 \times 6 = 90\). The perimeter trap is \(42\). Pro tip: area multiplies two dimensions and uses square units.

Example 4
Problem: A rectangle is \(8\) units long and \(8\) units wide. What is its area?
Answer: \(64\) square units
Solution: Area of a rectangle is length times width: \(8 \times 8 = 64\). The perimeter trap is \(32\). Pro tip: area multiplies two dimensions and uses square units.

Example 5
Problem: A rectangle is \(11\) units long and \(5\) units wide. What is its area?
Answer: \(55\) square units
Solution: Area of a rectangle is length times width: \(11 \times 5 = 55\). The perimeter trap is \(32\). Pro tip: area multiplies two dimensions and uses square units.

Example 6
Problem: A rectangle is \(18\) units long and \(3\) units wide. What is its area?
Answer: \(54\) square units
Solution: Area of a rectangle is length times width: \(18 \times 3 = 54\). The perimeter trap is \(42\). Pro tip: area multiplies two dimensions and uses square units.

Example 7
Problem: A rectangle is \(20\) units long and \(14\) units wide. What is its area?
Answer: \(280\) square units
Solution: Area of a rectangle is length times width: \(20 \times 14 = 280\). The perimeter trap is \(68\). Pro tip: area multiplies two dimensions and uses square units.

Example 8
Problem: A rectangle is \(13\) units long and \(7\) units wide. What is its area?
Answer: \(91\) square units
Solution: Area of a rectangle is length times width: \(13 \times 7 = 91\). The perimeter trap is \(40\). Pro tip: area multiplies two dimensions and uses square units.

Example 9
Problem: A rectangle is \(16\) units long and \(10\) units wide. What is its area?
Answer: \(160\) square units
Solution: Area of a rectangle is length times width: \(16 \times 10 = 160\). The perimeter trap is \(52\). Pro tip: area multiplies two dimensions and uses square units.

Example 10
Problem: A rectangle is \(25\) units long and \(4\) units wide. What is its area?
Answer: \(100\) square units
Solution: Area of a rectangle is length times width: \(25 \times 4 = 100\). The perimeter trap is \(58\). Pro tip: area multiplies two dimensions and uses square units.

Additional resources

• Formula card: rectangle area \(A=lw\), square area \(A=s^2\).
• Practice prompt: make two versions of the same rectangle problem, one asking for area and one asking for perimeter.