Perimeter, Area & Volume
Perimeter of Shapes
The perimeter is the total distance around a shape — add the lengths of all the sides. For a triangle with sides 3, 4 and 5 cm, the perimeter is 3 + 4 + 5 = 12 cm.
For regular shapes there are shortcuts: square perimeter = 4 × side, and rectangle perimeter = 2 × (length + breadth).
Example 1: Find the perimeter of a triangle with sides 3 cm, 4 cm and 5 cm.
3 + 4 + 5 = 12 cm.
Example 2: Find the perimeter of a rectangle 8 cm by 3 cm.
2 × (8 + 3) = 22 cm.
Quick recap
- Perimeter = sum of all sides.
- Square: 4 × side; rectangle: 2 × (length + breadth).
✓ Quick check
What is the perimeter of a square of side 6 cm?
4 × 6 = 24 cm.
A four-sided shape has sides 2, 3, 4 and 5 cm. What is its perimeter?
2 + 3 + 4 + 5 = 14 cm.
Area: Rectangle, Square, Triangle, Parallelogram
The area is the space inside a shape, in square units. Area of a rectangle = length × breadth, a square = side × side, a triangle = ½ × base × height, and a parallelogram = base × height.
Example 1: Find the area of a triangle with base 6 cm and height 4 cm.
½ × 6 × 4 = 12 sq cm.
Example 2: Find the area of a parallelogram with base 5 cm and height 4 cm.
5 × 4 = 20 sq cm.
Quick recap
- Rectangle: l × b; square: side × side.
- Triangle: ½ × base × height; parallelogram: base × height.
✓ Quick check
What is the area of a triangle with base 10 cm and height 6 cm?
½ × 10 × 6 = 30 sq cm.
What is the area of a parallelogram with base 8 cm and height 3 cm?
8 × 3 = 24 sq cm.
Volume of Cube & Cuboid
The volume is the space a solid takes up, measured in cubic units. Volume of a cuboid = length × breadth × height, and volume of a cube = side × side × side.
So a 2 × 3 × 4 cuboid has volume 24 cubic units, and a cube of side 3 has volume 27 cubic units.
Example 1: Find the volume of a cuboid 2 cm × 3 cm × 4 cm.
2 × 3 × 4 = 24 cubic cm.
Example 2: Find the volume of a cube of side 3 cm.
3 × 3 × 3 = 27 cubic cm.
Quick recap
- Cuboid volume = length × breadth × height.
- Cube volume = side × side × side.
✓ Quick check
What is the volume of a cube of side 2 cm?
2 × 2 × 2 = 8 cubic cm.
What is the volume of a cuboid 5 cm × 2 cm × 3 cm?
5 × 2 × 3 = 30 cubic cm.
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