Introduction
Area and Perimeter of Rectangles is an important Grade 4 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 and perimeter of rectangles.
What Is Area and Perimeter of Rectangles?
Area and Perimeter of Rectangles 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 and Perimeter of Rectangles
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: What is the area of the rectangle shown above?
- A. \(10\) sq cm
- B. \(20\) sq cm
- C. \(21\) sq cm
- D. \(28\) sq cm
Why it works: From the diagram, length is \(7\) cm and width is \(3\) cm. Area \(= 7 \times 3 = 21\) sq cm.
Answer: \(21\) sq cm
Visual Model 2
Question: What is the perimeter of the rectangle shown above?
- A. \(16\) in
- B. \(32\) in
- C. \(60\) in
- D. \(48\) in
Why it works: The rectangle is \(10\) in long and \(6\) in wide. Perimeter \(= 2(10) + 2(6) = 20 + 12 = 32\) in.
Answer: \(32\) in
Worked Examples
Example 1
Question: Each square in the grid above is \(1\) square unit. How many square units cover the rectangle?
- A. \(7\) sq units
- B. \(10\) sq units
- C. \(12\) sq units
- D. \(14\) sq units
- Count the grid squares: \(4\) columns \(\times\) \(3\) rows \(= 12\) square units.
Answer: \(12\) sq units
Example 2
Question: What is the area of the shaded rectangle above?
- A. \(9\) sq m
- B. \(18\) sq m
- C. \(20\) sq m
- D. \(25\) sq m
- From the diagram: length is \(5\) m and width is \(4\) m.
- Area \(= 5 \times 4 = 20\) sq m.
Answer: \(20\) sq m
Example 3
Question: Each small square is \(1\) square unit. What is the area of the rectangle?
- A. \(8\) sq units
- B. \(10\) sq units
- C. \(12\) sq units
- D. \(16\) sq units
- The grid shows \(6\) units by \(2\) units.
- Area \(= 6 \times 2 = 12\) sq units.
Answer: \(12\) sq units
Real-World Word Problems
Problem 1
Question: A garden is shaped like a rectangle. It is \(9\) feet long and \(5\) feet wide. How many feet of fencing are needed to go around the garden?
- A. \(14\) ft
- B. \(28\) ft
- C. \(45\) ft
- D. \(36\) ft
Why it works: To find how much fencing goes around the garden, we calculate perimeter: \(P = 2(9) + 2(5) = 18 + 10 = 28\) ft.
Answer: \(28\) ft
Problem 2
Question: What is the area of a rectangle that is \(10\) inches long and \(3\) inches wide?
- A. \(13\) sq in
- B. \(26\) sq in
- C. \(30\) sq in
- D. \(33\) sq in
Why it works: Area \(= \text{length} \times \text{width} = 10 \times 3 = 30\) sq in.
Answer: \(30\) sq in
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
A rectangle has a length of \(8\) ft and a width of \(5\) ft. What is its area?
- A. \(13\) sq ft
- B. \(26\) sq ft
- C. \(40\) sq ft
- D. \(45\) sq ft
Question 2
A rectangle has a length of \(12\) m and a width of \(7\) m. What is its perimeter?
- A. \(19\) m
- B. \(38\) m
- C. \(84\) m
- D. \(76\) m
Question 3
Diego draws a rectangle with a length of \(6\) cm and a width of \(4\) cm. What is the area of his rectangle?
- A. \(10\) sq cm
- B. \(20\) sq cm
- C. \(24\) sq cm
- D. \(30\) sq cm
Question 4
A poster is a rectangle with a length of \(11\) inches and a width of \(8\) inches. What is its perimeter?
- A. \(19\) in
- B. \(38\) in
- C. \(88\) in
- D. \(43\) in
Question 5
A room is \(15\) feet long and \(12\) feet wide. What is the area of the floor?
- A. \(27\) sq ft
- B. \(54\) sq ft
- C. \(180\) sq ft
- D. \(120\) sq ft
Question 6
Mia's bedroom window is a rectangle. The length is \(4\) feet and the width is \(3\) feet. What is the area of the window?
- A. \(7\) sq ft
- B. \(12\) sq ft
- C. \(14\) sq ft
- D. \(21\) sq ft
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(40\) sq ft
To find area, we multiply length times width: \(8 \times 5 = 40\) sq ft.
Question 2
Answer: \(38\) m
Perimeter is the distance around the rectangle. Use the formula \(P = 2\ell + 2w = 2(12) + 2(7) = 24 + 14 = 38\) m.
Question 3
Answer: \(24\) sq cm
Multiply length by width: \(6 \times 4 = 24\) sq cm.
Question 4
Answer: \(38\) in
The perimeter of the poster is \(P = 2(11) + 2(8) = 22 + 16 = 38\) in.
Question 5
Answer: \(180\) sq ft
The floor area is \(15 \times 12 = 180\) sq ft.
Question 6
Answer: \(12\) sq ft
Window area \(= 4 \times 3 = 12\) sq ft.
Connection to Standards
This lesson supports Grade 4 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 and Perimeter of Rectangles 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.
