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📐 Geometry & Area

Areas, perimeters, and shape properties

📐 Area of rectangles and triangles

Rectangle area = length × width. A rectangle 5 cm long and 3 cm wide has area 5 × 3 = 15 cm².

Triangle area = base × height ÷ 2. A triangle with base 6 cm and height 4 cm has area 6 × 4 ÷ 2 = 12 cm².

Key insight: A triangle is always exactly half of a rectangle with the same base and height. If you cut a rectangle diagonally, you get two equal triangles!

✂️ Cutting and rearranging shapes

If you cut a shape and rearrange the pieces, the total area stays the same. This powerful idea helps us find the area of irregular shapes.

Strategy: Split a tricky shape into rectangles and triangles you can measure easily. Then add up the areas.

Example: An L-shaped room is really two rectangles stuck together. Measure each rectangle separately, then add. If one part is 6 m × 4 m = 24 m² and the other is 3 m × 2 m = 6 m², the total is 30 m².

🔄 Perimeter tricks

Perimeter is the total distance around a shape. Walk around the edge and add up all the sides.

Key trick: If you push a dent in or out, the perimeter doesn't change (if horizontal and vertical distances stay the same). A staircase path around a rectangle has the same perimeter as the rectangle itself!

Example: A rectangle is 10 cm wide and 8 cm tall. Perimeter = 10 + 8 + 10 + 8 = 36 cm. Now imagine a wavy border following a staircase — same perimeter of 36 cm!

🧠 Practice Quiz

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