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💡 The Half-Rectangle Idea
Take any triangle. If you make a copy of it, flip it upside-down, and stick the two together, you always get a rectangle (or a parallelogram).
So one triangle is exactly half the area of that rectangle!
Triangle area = (rectangle area) ÷ 2 = (b × h) ÷ 2
🔄 Any Side Can Be the Base!
A triangle has three sides, so you can pick any of them as the base — just measure the height perpendicular from that side to the opposite corner. No matter which side you choose, you'll always get the same area, since a triangle only has one true area!
📏 Base and Height
Pick any side of the triangle as the base (b). The height (h) is the perpendicular distance from that base up to the opposite corner — straight up, not along a slanted side.
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Area of a triangle
Area = (base × height) ÷ 2 = (b × h) ÷ 2
Worked Example
Find the area of a triangle with base 10 cm and height 6 cm:
Step 1: Write the formula → Area = (b × h) ÷ 2
Step 2: Plug in → (10 × 6) ÷ 2
Step 3: Multiply first → 60 ÷ 2
Step 4: Divide → 30 cm² ✓
1 Use the Formula 📐
Multiply base × height, then divide by 2.
b = 8 cm, h = 4 cm
Step 1: 8 × 4 =
Step 2: ÷ 2 = cm²
b = 12 m, h = 5 m
Step 1: 12 × 5 =
Step 2: ÷ 2 = m²
b = 9 cm, h = 6 cm
Step 1:
Step 2: cm²
b = 14 m, h = 10 m
Step 1:
Step 2: m²
2 Quick Practice ⚡
Find the area in one line.
b = 6, h = 8
Area =
b = 20, h = 7
Area =
b = 11, h = 4
Area =
b = 16, h = 5
Area =
b = 9, h = 8
Area =
b = 13, h = 6
Area =
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📐 Right Triangles Are Easy
In a right triangle, the two sides that meet at the right angle (the "legs") are automatically the base and the height — they're already perpendicular to each other!
3 Right Triangles 📐
The two legs are the base and height. Find the area.
legs 3 cm and 4 cm
Area = (3 × 4) ÷ 2 = cm²
legs 5 m and 12 m
Area = m²
legs 8 cm and 15 cm
Area = cm²
legs 7 m and 6 m
Area = m²
4 Word Problems 📝
Use Area = (b × h) ÷ 2.
-
A triangular flag has base 30 cm and height 20 cm. What is its area?
Area = cm²
-
A garden is shaped like a triangle with base 8 m and height 5 m. How many m² is it?
Area = m²
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A triangular sail has base 12 m and height 9 m. What is its area?
Area = m²
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A triangle has area 24 cm² and base 8 cm. What is its height?
Hint: (8 × h) ÷ 2 = 24 → 8 × h = 48
height = cm
Answer Key:
1) 32→16; 60→30; 54→27; 140→70 —
2) 24, 70, 22, 40, 36, 39 —
3) 6, 30, 60, 21 —
4) 300 cm²; 20 m²; 54 m²; 6 cm