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Mensuration - Perimeter of Rectilinear Figures

Grade 6CBSE

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 (ll) and two shorter sides called breadth (bb).

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 (mmmm), centimeters (cmcm), meters (mm), or kilometers (kmkm). It represents a 1-dimensional length.

📐Formulae

Perimeter of a Rectangle = 2×(length+breadth)2 \times (length + breadth)

Perimeter of a Square = 4×side4 \times side

Perimeter of an Equilateral Triangle = 3×side3 \times side

Perimeter of a Regular Pentagon = 5×side5 \times side

Perimeter of a Regular Hexagon = 6×side6 \times side

Perimeter of any Regular Polygon = n×siden \times side (where nn is the number of sides)

💡Examples

Problem 1:

Find the perimeter of a rectangular field whose length is 150 m150\ m and breadth is 100 m100\ m.

Solution:

Given: Length (ll) = 150 m150\ m, Breadth (bb) = 100 m100\ m Perimeter of rectangle = 2×(l+b)2 \times (l + b) Perimeter = 2×(150+100) m2 \times (150 + 100)\ m Perimeter = 2×250 m2 \times 250\ m Perimeter = 500 m500\ m

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 120 m120\ m. If the cost of fencing is Rs 20Rs\ 20 per meter, find the total cost of fencing.

Solution:

Given: Side of square = 120 m120\ m Perimeter of square = 4×side=4×120=480 m4 \times side = 4 \times 120 = 480\ m Cost of fencing per meter = Rs 20Rs\ 20 Total cost = Perimeter×RatePerimeter \times Rate Total cost = 480×20=Rs 9,600480 \times 20 = Rs\ 9,600

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.