Area of Triangles

🎯 What Will We Learn Today?

We've learned to find the area of rectangles. Now let's learn the formula for the area of a triangle!

📚 How a Triangle Relates to a Rectangle

A triangle is exactly half of a rectangle! If you draw a diagonal line across a rectangle, you create two identical triangles.

That's why the area of a triangle is: A = ½ × base × height

📐 The Triangle Area Formula

A = ½ × b × h or A = (b × h) ÷ 2

Where:

b = base (the bottom side)

h = height (straight up from the base to the top point)

IMPORTANT: The height must be perpendicular (at a right angle) to the base!

🎮 Let's Calculate!

Example 1: A triangle has base 8 cm and height 5 cm.

A = (8 × 5) ÷ 2 = 40 ÷ 2 = 20 cm²

Example 2: The base is 12 inches and the height is 7 inches.

A = ½ × 12 × 7 = 6 × 7 = 42 in²

Example 3: Compare: rectangle 6×4 vs. triangle with same base and height.

Rectangle: 6 × 4 = 24

Triangle: (6 × 4) ÷ 2 = 12

The triangle is exactly half! ✓

💡 Visual Proof

Draw a rectangle. Cut it diagonally from one corner to the opposite corner. You now have two triangles. Each triangle takes up half the rectangle's area!

📝 Practice Problems

Find the area of a triangle with base 10 cm and height 6 cm.

A triangle has base 14 m and height 9 m. What is its area?

If a triangle's area is 20 cm² and its base is 8 cm, what is its height?

A rectangle has length 12 and width 5. What's the area of each triangle if you cut it diagonally?

🎮 Play a Game!

Practice with Tractor Multiplication — multiply and pull!