Geometric Measurement | Fourth Grade

Complete Notes & Formulas

1. Perimeter of Rectangles

Definition: The perimeter of a rectangle is the total distance around the outside of the rectangle. It is the sum of all four sides.

📐 Key Formulas:

Perimeter = 2 × (Length + Width)

P = 2(l + w)

OR: P = l + w + l + w

📝 Steps to Find Perimeter:

Identify the length and width of the rectangle
Add length and width
Multiply the sum by 2
Write the answer with units (cm, m, etc.)

✏️ Examples:

Example 1:

Length = 12 cm, Width = 8 cm

P = 2(12 + 8)

P = 2(20) = 40 cm

Answer: 40 cm

Example 2:

Length = 15 m, Width = 10 m

P = 15 + 10 + 15 + 10 = 50 m

Answer: 50 m

2. Perimeter of Polygons

Definition: The perimeter of any polygon is the sum of the lengths of all its sides. Add up all the side lengths to get the perimeter.

📐 General Formula:

Perimeter = Sum of All Sides

📊 Specific Polygon Formulas:

Polygon	Perimeter Formula
Triangle	P = a + b + c
Square	P = 4 × side
Rectangle	P = 2(l + w)
Pentagon (regular)	P = 5 × side
Hexagon (regular)	P = 6 × side

✏️ Example:

Find the perimeter of a pentagon with sides: 5 cm, 6 cm, 7 cm, 5 cm, 6 cm

P = 5 + 6 + 7 + 5 + 6 = 29 cm

Answer: 29 cm

🔑 For Regular Polygons:

P = Number of Sides × Length of One Side

3. Perimeter of Rectilinear Shapes

Definition: Rectilinear shapes are made up of straight lines (rectangles joined together). They look like "L" shapes, "T" shapes, or step patterns. To find the perimeter, add all the outside edge lengths.

📐 Formula:

Perimeter = Sum of All Outer Edges

📝 Steps to Find Perimeter:

Step 1: Identify all the outer edges of the shape
Step 2: If any side length is missing, calculate it using opposite sides
Step 3: Add all the side lengths together
Step 4: Include units in your answer

✏️ Example:

L-shaped figure with sides: 8 cm, 3 cm, 5 cm, 2 cm, 3 cm, 5 cm

P = 8 + 3 + 5 + 2 + 3 + 5 = 26 cm

Answer: 26 cm

💡 Important Tip:

In rectilinear shapes, opposite sides often help you find missing lengths!

4. Perimeter: Find the Missing Side Length

Definition: When the perimeter and some side lengths are known, you can find the missing side by subtracting the known sides from the total perimeter.

🔑 Key Formula:

Missing Side = Perimeter - Sum of Known Sides

📝 Steps:

Write down the total perimeter
Add all the known side lengths
Subtract the sum from the perimeter
The result is the missing side length

✏️ Examples:

Example 1: Rectangle

Perimeter = 36 cm, Width = 7 cm, Length = ?

Solution:

P = 2(l + w)

36 = 2(l + 7)

18 = l + 7

l = 18 - 7 = 11 cm

Answer: 11 cm

Example 2: Triangle

Perimeter = 25 cm, Two sides = 8 cm and 10 cm, Third side = ?

Solution:

Missing side = 25 - (8 + 10)

Missing side = 25 - 18 = 7 cm

Answer: 7 cm

5. Use Perimeter to Determine Cost

Definition: Real-world applications of perimeter involve calculating costs for materials like fencing, borders, frames, or ribbon that go around the edge of a shape.

🔑 Key Formula:

Total Cost = Perimeter × Cost per Unit

📝 Steps:

Find the perimeter of the shape
Identify the cost per unit (per meter, per cm, etc.)
Multiply perimeter by cost per unit
Write answer with currency symbol

✏️ Example:

Problem: A rectangular garden is 15 m long and 10 m wide. Fencing costs ₹50 per meter. What is the total cost?

Solution:

Step 1: Find perimeter

P = 2(15 + 10) = 2(25) = 50 m

Step 2: Calculate cost

Total Cost = 50 × ₹50 = ₹2,500

Answer: ₹2,500

6. Find the Area of Figures Made of Unit Squares

Definition: Area is the amount of space inside a 2D shape. A unit square is a square with sides of 1 unit. To find area, count how many unit squares fit inside the shape.

📐 Key Concept:

Area = Number of Unit Squares

Units: square units (sq. cm, sq. m, cm², m²)

📝 How to Count:

Look at the grid inside the shape
Count all the complete unit squares
If there are partial squares, estimate or combine
Write answer in square units

✏️ Example:

A shape has 4 rows of unit squares with 6 squares in each row

Area = 4 × 6 = 24 square units

Answer: 24 sq. units

7-9. Select & Create Figures with Given Area

Definition: Different shapes can have the same area. Understanding this helps identify, compare, and create shapes with specific area requirements.

💡 Important Concepts:

Same area doesn't mean same shape
Rectangles with area 12: 1×12, 2×6, 3×4
Different perimeters can have same area
Same perimeter can have different areas

✏️ Examples:

Example 1: Create shapes with area 16 sq. units

• Rectangle: 4 × 4 (square)

• Rectangle: 2 × 8

• Rectangle: 1 × 16

All have area = 16 sq. units!

Example 2: Which shapes have area 20 sq. units?

Shape A: 5 × 4 = 20 ✓

Shape B: 10 × 2 = 20 ✓

Shape C: 3 × 6 = 18 ✗

10. Find Area or Missing Side Length of Rectangle

Definition: The area of a rectangle is found by multiplying length and width. If area and one dimension are known, you can find the missing dimension.

📐 Key Formulas:

Area = Length × Width

Length = Area ÷ Width

Width = Area ÷ Length

✏️ Examples:

Example 1: Find Area

Length = 9 cm, Width = 7 cm

Area = 9 × 7 = 63 cm²

Answer: 63 cm²

Example 2: Find Missing Length

Area = 72 m², Width = 8 m, Length = ?

Length = 72 ÷ 8 = 9 m

Answer: 9 m

Example 3: Find Missing Width

Area = 56 cm², Length = 8 cm, Width = ?

Width = 56 ÷ 8 = 7 cm

Answer: 7 cm

11. Area and Perimeter: Word Problems

Definition: Real-world problems involving both area and perimeter require reading carefully to determine which measurement is needed.

🔑 When to Use What:

Use PERIMETER for:

• Fencing, borders, frames

• Going AROUND the outside

• Ribbon, rope, string

Use AREA for:

• Covering, painting, carpet

• Space INSIDE

• Tiles, grass, flooring

✏️ Word Problems:

Problem 1: Carpeting a Room

A room is 12 m long and 8 m wide. How much carpet is needed?

Solution:

This asks for covering → Use AREA

Area = 12 × 8 = 96 m²

Answer: 96 m² of carpet

Problem 2: Fencing a Garden

A rectangular garden is 20 m long and 15 m wide. How much fencing is needed?

Solution:

Fencing goes around → Use PERIMETER

P = 2(20 + 15) = 2(35) = 70 m

Answer: 70 m of fencing

Problem 3: Combined Problem

A park is 50 m × 30 m. Find (a) area for grass and (b) perimeter for fence.

Solution:

(a) Area = 50 × 30 = 1,500 m²

(b) Perimeter = 2(50 + 30) = 160 m

Answers: 1,500 m² grass; 160 m fence

📝 Problem-Solving Steps:

Read the problem carefully
Identify if it's asking for area or perimeter
Write down known measurements
Use the correct formula
Calculate and check units

Geometric Measurement Quick Reference

Concept	Formula	Units
Perimeter Rectangle	P = 2(l + w)	cm, m, etc.
Perimeter Square	P = 4 × side	cm, m, etc.
Perimeter Polygon	P = Sum of all sides	cm, m, etc.
Area Rectangle	A = l × w	cm², m², sq. units
Area Square	A = side × side	cm², m², sq. units
Missing Side (Perimeter)	Side = P - other sides	Same as given
Missing Side (Area)	Length = A ÷ Width	Same as given
Total Cost	Cost = P × price/unit	Currency (₹, $)