Solved Exercises on Area and Perimeter Word Problems in Grade 4

Master area and perimeter calculations: rectangles, squares, and real-world applications through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Rectangle Area and Perimeter
Exercise 1
A rectangular garden has a length of 12 feet and a width of 8 feet. Find the area and perimeter of the garden.
Definitions:

Area: The space inside a shape measured in square units

Perimeter: The distance around the outside of a shape

Rectangle: A 4-sided shape with 4 right angles

Calculation method:
  1. Identify the length and width of the rectangle
  2. Apply the area formula: Area = Length × Width
  3. Apply the perimeter formula: Perimeter = 2 × (Length + Width)
Given
Length = 12 ft, Width = 8 ft
Area
12 × 8 = 96 ft²
Perimeter
2(12 + 8) = 40 ft
Step 1: Identify dimensions

Length = 12 feet, Width = 8 feet

Step 2: Calculate area

Area = Length × Width = 12 × 8 = 96 square feet

Step 3: Calculate perimeter

Perimeter = 2 × (Length + Width) = 2 × (12 + 8) = 2 × 20 = 40 feet

Area = 96 ft², Perimeter = 40 ft
Final answer:

The area of the garden is 96 square feet and the perimeter is 40 feet.

Applied rules:

• Area of rectangle: Length × Width

• Perimeter of rectangle: 2 × (Length + Width)

• Units: Area is in square units, perimeter is in linear units

2 Square Area and Perimeter
Exercise 2
A square playground has sides measuring 15 meters. Find the area and perimeter of the playground.
Definition:

Square: A 4-sided shape with all sides equal and 4 right angles

Given
Side = 15 m
Area
15² = 225 m²
Perimeter
4 × 15 = 60 m
Step 1: Identify side length

All sides of a square are equal: Side = 15 meters

Step 2: Calculate area

Area = Side × Side = 15 × 15 = 225 square meters

Step 3: Calculate perimeter

Perimeter = 4 × Side = 4 × 15 = 60 meters

Area = 225 m², Perimeter = 60 m
Final answer:

The area of the playground is 225 square meters and the perimeter is 60 meters.

Applied rules:

• Area of square: Side × Side = Side²

• Perimeter of square: 4 × Side

• Square property: All 4 sides are equal

3 Finding Missing Dimension
Exercise 3
A rectangular room has an area of 60 square feet. If the width is 5 feet, what is the length? Also find the perimeter.
Definition:

Missing dimension: When one measurement is unknown, use known measurements to solve

Given
Area = 60 ft², Width = 5 ft
Formula
Length = Area ÷ Width
Result
Length = 12 ft, Perimeter = 34 ft
Step 1: Use area formula to find length

Area = Length × Width

60 = Length × 5

Length = 60 ÷ 5 = 12 feet

Step 2: Calculate perimeter

Perimeter = 2 × (Length + Width) = 2 × (12 + 5) = 2 × 17 = 34 feet

Step 3: Verify the solution

Area = 12 × 5 = 60 square feet ✓

Length = 12 ft, Perimeter = 34 ft
Final answer:

The length of the room is 12 feet and the perimeter is 34 feet.

Applied rules:

• Find missing dimension: Length = Area ÷ Width

• Perimeter formula: 2 × (Length + Width)

• Verification: Check that calculated dimensions match given area

Formulas and Methods
Area = Length × Width
Rectangle Area
Perimeter = 2(Length + Width)
Rectangle Perimeter
Area = Side²
Square Area
Perimeter = 4 × Side
Square Perimeter
Key definitions:

Area: The amount of space inside a 2D shape measured in square units

Perimeter: The total distance around the edge of a shape

Rectangle: A quadrilateral with 4 right angles and opposite sides equal

Square: A rectangle with all sides equal

Problem-solving method:
  1. Read carefully: Identify what is given and what is asked
  2. Draw a diagram: Sketch the shape with given measurements
  3. Choose formula: Select the correct area or perimeter formula
  4. Calculate: Substitute values and perform operations
  5. Check: Verify your answer makes sense
Tip 1: Always include units in your answer (ft² for area, ft for perimeter).
Tip 2: Area answers are always in square units.
Tip 3: Perimeter answers are always in linear units.
Tip 4: Draw the shape to visualize the problem.
Common errors: Forgetting to multiply by 2 in perimeter formula, confusing area and perimeter formulas.
Memorization tip: Remember "Area = Inside, Perimeter = Outside".
Key Concepts and Properties
Area = Length × Width
Rectangle Area Formula
Rectangle Area
A = L × W
Length × Width
Rectangle Perimeter
P = 2(L + W)
2 × (Length + Width)
Square Area
A = s²
Side × Side
Square Perimeter
P = 4s
4 × Side
Important properties:

Rectangle: Opposite sides are equal and parallel, all angles are 90°

Square: All sides are equal, all angles are 90°

Area: Measures the surface inside a shape

Perimeter: Measures the boundary of a shape

Word problem strategy:
  1. Understand: Read the problem completely
  2. Identify: Find given information and what's needed
  3. Plan: Choose the right formula
  4. Solve: Perform calculations step by step
  5. Check: Verify your answer is reasonable
Tip 1: Label your diagram with given measurements.
Tip 2: For missing dimensions, rearrange the area formula.
Tip 3: Always write the formula before substituting values.
Essential formulas to remember:

• Rectangle Area: A = Length × Width

• Rectangle Perimeter: P = 2 × (Length + Width)

• Square Area: A = Side × Side = Side²

• Square Perimeter: P = 4 × Side

• Finding missing dimension: Length = Area ÷ Width

Visual aid: Rectangle has length and width
Visual aid: Square has all sides equal

Questions & Answers

Question: I always get confused between area and perimeter. How can I remember which is which?

Answer: Great question! Here are some memory tricks:

  • Area = "A" is for "Inside" - Think of the "inside" of a shape where you'd spread grass seed or paint a wall
  • Perimeter = "P" is for "Perimeter" or "Path" - Think of walking around the "outside" edge of a shape
  • Remember: Area is "covering" (like a carpet), Perimeter is "fencing" (like going around the yard)

Another way: Area answers end in square units (ft², m²), while Perimeter answers end in linear units (ft, m).

Try this: Draw a rectangle on paper. Shade the inside to represent area. Trace around the outside to represent perimeter.

Question: In exercise 3, why did we divide the area by the width to find the length?

Answer: This uses the relationship between area and dimensions:

  • We know the formula: Area = Length × Width
  • If we know Area and Width, we can rearrange the formula to find Length
  • Starting with: Area = Length × Width
  • Divide both sides by Width: Area ÷ Width = Length

Think of it like this: If you know the total area of tiles (60 square feet) and the width (5 feet), then the length must be how many rows of 5 fit into 60, which is 60 ÷ 5 = 12 feet.

This is called "working backwards" from the formula.

Question: Why does the perimeter formula have a 2 in it for rectangles? Why not just add the length and width?

Answer: The perimeter is the total distance around the rectangle. A rectangle has 4 sides:

  • One length along the top
  • One width along the right side
  • One length along the bottom
  • One width along the left side

So the perimeter is: Length + Width + Length + Width

We can group these: Length + Length + Width + Width = 2×Length + 2×Width = 2×(Length + Width)

That's why we multiply by 2 in the formula: P = 2×(L + W)

Try counting the sides of a rectangle you draw - you'll see there are 2 lengths and 2 widths!