PerimeterandArea

Imagine you’re setting up a garden and need to fence its boundary or lay down grass. How would you figure out the amount of fencing or grass required? That’s where perimeter and area come in handy. Let’s explore how to calculate these for simple shapes!

Contents

• What are Perimeter and Area?
  • Key Differences
• Perimeter and Area of a Square
• Perimeter and Area of a Rectangle
• Perimeter and Area of a Triangle
• Quiz: Test Your Knowledge
• Key Takeaways

What are Perimeter and Area?

Definition:

• Perimeter is the total distance around a shape. It’s the sum of the lengths of all the sides.
• Area is the amount of space inside a shape. It’s measured in square units.

Key Differences

• Perimeter measures the boundary, while area measures the surface.
• Units for perimeter are linear (e.g., cm, m), whereas area is in square units (e.g., cm², m²).

Perimeter and Area of a Square

A square has four equal sides.

Formulas:

• Perimeter: , where is the side length.
• Area:

Example:

If the side length of a square is 4 cm:

• Perimeter: cm
• Area: cm²

Perimeter and Area of a Rectangle

A rectangle has opposite sides that are equal.

Formulas:

• Perimeter: , where is the length and is the width.
• Area:

Example:

If a rectangle has a length of 8 cm and a width of 3 cm:

• Perimeter: cm
• Area: cm²

Perimeter and Area of a Triangle

A triangle has three sides and three angles.

Observation: A triangle can be thought of as half a rectangle. If you draw a diagonal across a rectangle, it divides the rectangle into two triangles. This is why the area formula for a triangle includes the factor .

Formulas:

• Perimeter: , where , , and are the lengths of the sides.
• Area: For a triangle with a base and height ,

Example:

If a triangle has sides of 6 cm, 7 cm, and 5 cm, and its height is 4 cm:

• Perimeter: cm
• Area: cm²

Image:

Quiz: Test Your Knowledge

Key Takeaways

• Perimeter is the total length around a shape, while area is the space inside it.
• Square: ,
• Rectangle: ,
• Triangle: ,
• Understanding these concepts is essential for practical applications like construction, design, and more.