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Mensuration - Perimeter of Rectangles and Regular Polygons

Grade 6ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Perimeter is the total length of the boundary of a closed plane figure. Visually, imagine walking along the edges of a shape from a starting corner and returning to the same spot; the total distance you walk is the perimeter.

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The perimeter is a linear measurement and is expressed in standard units of length such as millimeters (mmmm), centimeters (cmcm), meters (mm), or kilometers (kmkm). All dimensions must be converted to the same unit before calculation.

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A rectangle is a four-sided figure where opposite sides are equal and parallel. It has a length (ll) and a breadth (bb). The perimeter is the sum of these four sides (l+b+l+bl + b + l + b), which simplifies to two sets of length plus breadth.

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A square is a regular quadrilateral where all four sides are of equal length (ss). Visually, it appears as a perfectly symmetrical box, and its perimeter is the total length of these four identical segments.

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Regular polygons are closed shapes where all sides are equal in length and all interior angles are equal. Examples include equilateral triangles (3 sides), regular pentagons (5 sides), and regular hexagons (6 sides).

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The perimeter of any regular polygon is calculated by multiplying the length of one side by the total number of sides. Visually, this is like adding the same side length repeatedly for as many sides as the shape has.

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To find the side of a regular polygon when the perimeter is known, you perform the inverse operation: divide the total perimeter by the number of sides (nn).

📐Formulae

Perimeter of a Rectangle=2×(l+b)\text{Perimeter of a Rectangle} = 2 \times (l + b) where ll is length and bb is breadth

Perimeter of a Square=4×s\text{Perimeter of a Square} = 4 \times s where ss is the length of a side

Perimeter of an Equilateral Triangle=3×s\text{Perimeter of an Equilateral Triangle} = 3 \times s

Perimeter of a Regular Pentagon=5×s\text{Perimeter of a Regular Pentagon} = 5 \times s

Perimeter of a Regular Hexagon=6×s\text{Perimeter of a Regular Hexagon} = 6 \times s

Perimeter of a Regular Polygon=n×s\text{Perimeter of a Regular Polygon} = n \times s where nn is the number of sides

Side of a Regular Polygon=Perimetern\text{Side of a Regular Polygon} = \frac{\text{Perimeter}}{n}

💡Examples

Problem 1:

Calculate the perimeter of a rectangular park whose length is 45 m45\text{ m} and breadth is 32 m32\text{ m}.

Solution:

Given: Length (ll) = 45 m45\text{ m} Breadth (bb) = 32 m32\text{ m}

Using the formula: Perimeter=2×(l+b)\text{Perimeter} = 2 \times (l + b) Perimeter=2×(45+32)\text{Perimeter} = 2 \times (45 + 32) Perimeter=2×77\text{Perimeter} = 2 \times 77 Perimeter=154 m\text{Perimeter} = 154\text{ m}

Explanation:

To find the perimeter of a rectangle, we first add the length and the breadth together to find the sum of two adjacent sides. Then, we multiply that sum by 2 to include the other two equal opposite sides.

Problem 2:

The perimeter of a regular pentagon is 65 cm65\text{ cm}. Find the length of each side.

Solution:

Given: Perimeter (PP) = 65 cm65\text{ cm} Number of sides (nn) for a pentagon = 55

Using the formula: Side(s)=Perimetern\text{Side} (s) = \frac{\text{Perimeter}}{n} s=655s = \frac{65}{5} s=13 cms = 13\text{ cm}

Explanation:

Since a regular pentagon has 5 sides of equal length, we divide the total perimeter by 5 to find the length of one individual side.