Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Perimeter is the total length of the boundary of a closed figure. Imagine starting at one corner of a shape and walking along the edges until you return to the starting point; the total distance you walked is the perimeter.
Rectilinear figures are plane figures bounded by straight line segments. Visually, these include shapes like triangles, rectangles, and squares, where every side is a straight line and the figure is completely closed.
A rectangle is a four-sided figure where the opposite sides are equal and parallel. Visually, it has two longer sides called length () and two shorter sides called breadth ().
A square is a specific type of rectangle where all four sides are of equal length. Visually, it appears perfectly balanced and symmetrical because every side looks exactly the same.
Regular polygons are figures where all sides are of equal length and all angles are equal. Examples include equilateral triangles (3 equal sides), regular pentagons (5 equal sides), and regular hexagons (6 equal sides).
The perimeter of any general rectilinear figure (irregular shape) is calculated by simply adding the lengths of all its individual sides together.
Perimeter is measured in linear units such as millimeters (), centimeters (), meters (), or kilometers (). It represents a 1-dimensional length.
📐Formulae
Perimeter of a Rectangle =
Perimeter of a Square =
Perimeter of an Equilateral Triangle =
Perimeter of a Regular Pentagon =
Perimeter of a Regular Hexagon =
Perimeter of any Regular Polygon = (where is the number of sides)
💡Examples
Problem 1:
Find the perimeter of a rectangular field whose length is and breadth is .
Solution:
Given: Length () = , Breadth () = Perimeter of rectangle = Perimeter = Perimeter = Perimeter =
Explanation:
Since the field is rectangular, we apply the formula for the perimeter of a rectangle which accounts for two lengths and two breadths.
Problem 2:
A farmer wants to fence a square garden of side . If the cost of fencing is per meter, find the total cost of fencing.
Solution:
Given: Side of square = Perimeter of square = Cost of fencing per meter = Total cost = Total cost =
Explanation:
Fencing is always done along the boundary, so we first calculate the perimeter of the square garden and then multiply that total length by the rate per meter.