Introduction
Area by Multiplying Side Lengths is an important Grade 3 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with area by multiplying side lengths.
What Is Area by Multiplying Side Lengths?
Area by Multiplying Side Lengths means measuring how much flat space a figure covers by using equal-sized square units.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Area by Multiplying Side Lengths
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Use square units that cover the figure without gaps or overlaps.
- Count rows and columns when the unit squares are arranged in an array.
- Connect repeated addition to multiplication when finding area.
- Break complex figures into smaller rectangles when that makes the work clearer.
Visual Models
Visual Model 1
Question: A rectangular rug is \(6\) meters long and \(4\) meters wide. What is the area of the rug?
- A. \(10\) sq m
- B. \(24\) sq m
- C. \(20\) sq m
- D. \(12\) sq m
Why it works: Area \(=\) length \(\times\) width \(=6\times4=24\) square meters. Choice A (10) is the sum; C (20) is 4×5 miscomputation; D (12) is 6×2.
Answer: \(24\) sq m
Visual Model 2
Question: What is the area of this rectangle?
- A. \(8\) sq in
- B. \(15\) sq in
- C. \(10\) sq in
- D. \(12\) sq in
Why it works: Area \(=\) length \(\times\) width \(=5\times3=15\) square inches. Choice A (8) is the sum; C (10) is \(5\times2\); D (12) is \(4\times3\).
Answer: \(15\) sq in
Worked Examples
Example 1
Question: Find the area of the rectangle shown above.
- A. \(6\) sq cm
- B. \(8\) sq cm
- C. \(4\) sq cm
- D. \(12\) sq cm
- Area \(=\) length \(\times\) width \(=4\times2=8\) square centimeters.
- Choice A (6) is the sum; C (4) is one dimension; D (12) is \(4\times3\).
Answer: \(8\) sq cm
Example 2
Question: Lily is building a sandbox for her backyard. The sandbox is \(8\) feet long and \(6\) feet wide. What is the area of the sandbox?
- A. \(48\) sq ft
- B. \(28\) sq ft
- C. \(14\) sq ft
- D. \(56\) sq ft
- Area \(=\) length \(\times\) width \(=8\times6=48\) square feet.
Answer: \(48\) sq ft
Example 3
Question: A rectangular parking spot measures \(6\) meters by \(4\) meters. What is its area?
- A. \(10\) sq m
- B. \(20\) sq m
- C. \(12\) sq m
- D. \(24\) sq m
- Area \(=\) length \(\times\) width \(=6\times4=24\) square meters.
Answer: \(24\) sq m
Real-World Word Problems
Problem 1
Question: A garden is \(7\) feet long and \(5\) feet wide. What is its area?
- A. \(12\) sq ft
- B. \(35\) sq ft
- C. \(24\) sq ft
- D. \(70\) sq ft
Why it works: Area \(=\) length \(\times\) width \(=7\times5=35\) square feet. Choice A (12) is the sum \(7+5\); Choice C (24) is common product error; Choice D (70) is double the area.
Answer: \(35\) sq ft
Problem 2
Question: A classroom floor is shaped like a rectangle with a length of \(9\) feet and a width of \(8\) feet. What is the area of the classroom floor?
- A. \(17\) sq ft
- B. \(72\) sq ft
- C. \(64\) sq ft
- D. \(63\) sq ft
Why it works: Area \(=\) length \(\times\) width \(=9\times8=72\) square feet. Choice A (17) is the sum; C (64) is \(8\times8\); D (63) is \(9\times7\).
Answer: \(72\) sq ft
Common Mistakes
- Counting only the outside squares instead of all squares inside the figure.
- Leaving gaps or overlaps when using unit squares.
- Multiplying side lengths before checking whether the figure is a rectangle.
- Forgetting to write square units with an area answer.
Strategy Tips
- Trace the rectangle or figure before counting.
- Use rows and columns to organize unit squares.
- Write an equation after the model makes sense.
- Check whether the answer needs square units.
Practice Questions
Question 1
Sam needs to paint a poster that is \(10\) inches wide and \(8\) inches tall. What is the total area Sam needs to paint?
- A. \(36\) sq in
- B. \(80\) sq in
- C. \(18\) sq in
- D. \(90\) sq in
Question 2
A rectangular tile is \(7\) inches long and \(3\) inches wide. How much area does one tile cover?
- A. \(20\) sq in
- B. \(28\) sq in
- C. \(21\) sq in
- D. \(10\) sq in
Question 3
Noah is making a rectangular picture frame. The frame is \(9\) inches wide and \(7\) inches tall. What is the area inside the frame?
- A. \(32\) sq in
- B. \(56\) sq in
- C. \(16\) sq in
- D. \(63\) sq in
Question 4
What is the area of the rectangle shown?
- A. \(7\) sq cm
- B. \(14\) sq cm
- C. \(12\) sq cm
- D. \(10\) sq cm
Question 5
A rectangular rug has an area of \(36\) square feet. If the width is \(4\) feet, what is the length?
- A. \(9\) feet
- B. \(8\) feet
- C. \(40\) feet
- D. \(32\) feet
Question 6
A rectangular pool is \(6\) meters long and \(3\) meters wide. Find its area.
- A. \(9\) sq m
- B. \(36\) sq m
- C. \(15\) sq m
- D. \(18\) sq m
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(80\) sq in
Area \(=\) width \(\times\) height \(=10\times8=80\) square inches.
Question 2
Answer: \(21\) sq in
Area \(=\) length \(\times\) width \(=7\times3=21\) square inches.
Question 3
Answer: \(63\) sq in
Area \(=\) width \(\times\) height \(=9\times7=63\) square inches.
Question 4
Answer: \(10\) sq cm
Area \(=\) length \(\times\) width \(=5\times2=10\) square centimeters.
Question 5
Answer: \(9\) feet
Area \(=\) length \(\times\) width, so \(36 = \text{length} \times 4\). Therefore, length \(=36\div4=9\) feet. Choice B (8) is a common error; C (40) confuses with perimeter; D (32) is area minus width.
Question 6
Answer: \(18\) sq m
Area \(=\) length \(\times\) width \(=6\times3=18\) square meters.
Connection to Standards
This lesson supports Grade 3 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Area by Multiplying Side Lengths becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Area means every square unit inside the figure.
