🟧 Area of a Square

Lesson 1 — What is area, and how do we measure it?

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💡 What Is Area?
Area is the amount of space inside a flat shape. We measure area by counting how many unit squares fit inside the shape.

A unit square is a square that measures 1 unit on each side. Its area is 1 square unit (we write it as 1 unit² or, for centimeters, 1 cm²).
Counting Unit Squares Inside a Square
4 units
A 4 × 4 square holds 16 unit squares → area = 16 unit²
1 Count the Unit Squares 🔢
Each grid below is a square. Count the unit squares to find the area.

2 × 2 square
unit squares inside:
Area = unit²

3 × 3 square
unit squares inside:
Area = unit²

5 × 5 square
unit squares inside:
Area = unit²

🟧 Area of a Square

Use the shortcut: side × side ⚡

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📏 The Formula
Counting every square would take forever for a big shape! Luckily there's a shortcut.
A square has all 4 sides equal. If one side is s, the rows make s columns of s unit squares.
Area of a square with side s Area = s × s = s²
Worked Example
Find the area of a square with side 6 cm:
Step 1: Write the formula → Area = s × s
Step 2: Replace s with 6 → 6 × 6
Step 3: Calculate → 36 cm² ✓
2 Use the Formula 📐
Find the area of each square using Area = s × s.
side = 4 cm
Area = 4 × 4 = cm²
side = 7 m
Area = × = m²
side = 9 cm
Area = × = cm²
side = 12 m
Area = × = m²
side = 10 cm
Area = cm²
side = 15 m
Area = m²

🟧 Area of a Square

Word problems and going backwards! 🧠

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🔁 Going Backwards
If you know the area of a square but not the side, ask: what number times itself gives this area?
Example: Area = 25 cm² → side × side = 25 → side = 5 cm (because 5 × 5 = 25).
3 Find the Missing Side 🔍
Which number times itself gives the area?
Area = 16 cm² → side = cm
Area = 49 m² → side = m
Area = 81 cm² → side = cm
Area = 100 m² → side = m
4 Word Problems 📝
Read carefully, then use Area = s × s.
Answer Key: 1) 4, 9, 25 — 2) 16; 7×7=49; 9×9=81; 12×12=144; 100; 225 — 3) 4, 7, 9, 10 — 4) 64 m²; 400 cm²; 121 m²; 8 cm