Perimeter of Closed Figures

The reading material provided on this page for Perimeter of Closed Figures is specifically designed for students in grades 5 and 6. So, let's begin!

What is Closed Figure?

A closed figure is a shape where all of the points along the boundary are connected, forming a continuous loop with no gaps or holes, where the starting and ending points of the boundary are the same. This means closed figures refer to shapes or objects that have a complete boundary that encloses an area.

Examples of closed figures include circles, squares, rectangles, triangles, and polygons.

Perimeter of Closed Figures

Perimeter of a Triangle

The perimeter of a triangle is the total length of all three sides of the triangle.

Example: Consider a triangle with sides of length 5 cm, 7 cm and 9 cm.

Solution: The perimeter of this triangle would be: 5 cm + 7 cm + 9 cm = 21 cm
So, the perimeter of this triangle is 21 cm.

Perimeter of a Quadrilateral

The perimeter of a quadrilateral is the sum of the lengths of its four sides. It can be calculated by adding the length of each side of the quadrilateral together.

Example: Consider a quadrilateral with four sides a, b, c, d are 7 cm, 9 cm, 5 cm and 16 cm respectively. Find its Perimeter?

Solution: To find the Perimeter of this rectangle, we need to add the lengths of all four sides.
P = a + b + c + d
P = 7 + 9 + 5 + 16
P = 37 cm

So, the perimeter of the quadrilateral is 37 cm.

Perimeter of a Rectangle

The perimeter of a rectangle is the total length of all four sides of the rectangle. It is calculated by adding the lengths of all four sides.

Example: Consider a rectangle with length = 8 units and width = 4 units.

Solution: To find the perimeter of this rectangle, we need to add the lengths of all four sides:
P = 2 x (8) + 2 x (4)
P = 16 + 8
P = 24 units

So, the perimeter of the rectangle is 24 units.

Perimeter of a Square

The perimeter of a square is the total length of all four sides of the square.

Example: Let's assume we have a square with sides measuring 4 cm each.

Solution: To find the Perimeter, we add up the length of all four sides:
P = 4 x side
= 4 x 4 = 16 cm

So, the perimeter of this square is 16 cm.

Perimeter of a Circle

The perimeter of a circle is the distance around the outside edge of the circle. It is also known as its circumference. It can be calculated using the formula:

C = 2 π r

Where:
C = circumference
π = pi (approximated as 3.14)
r = radius (the distance from the centre of the circle to the boundary of the circle)

Example: Let's say we have a circle with a radius of 5 cm.

Solution: To find the circumference, we would use the formula:
C = 2 π r
= 2 x 3.14 x 5
= 31.4 cm

So, the Perimeter (circumference) of the circle with a radius of 5 cm is 31.4 cm.

Perimeter of a Polygon

The perimeter of a polygon is the total length of its sides, which is the sum of the lengths of all its sides. The formula for the Perimeter of a polygon depends on the number and lengths of its sides.

For a regular polygon with n sides, each of length s, the formula for the perimeter is:

Perimeter = Number of sides x length of sides

= n×s

Example: A pentagon with a side length of 4 units.

Solution: Perimeter = 5 x 4 = 20 cm

For an irregular polygon with different side lengths, the formula for the perimeter is:
Perimeter = s₁ + s₂ + s₃ + ... + s_n
where s₁, s₂, s₃, ..., s_n are the lengths of the polygon's sides.

Example: A pentagon with side lengths of 4 cm, 6 cm, 4 cm, 5 cm and 8 cm.

Solution: Perimeter = s₁ + s₂ + s₃ + s₄ + s₅
Perimeter = 4 + 6 + 4 + 5 + 8
= 27 cm

Perimeter of a Parallelogram

The perimeter of a parallelogram is the sum of the lengths of all four sides.

Example: Let's consider a parallelogram with sides measuring 8 units and 10 units.

Solution: The perimeter of the parallelogram can be calculated as follows:
P = 2 x (a + b)
= 2 x (8 + 10)
= 2 x 18
= 36 units

So, the perimeter of the parallelogram is 36 units.

Perimeter of a Trapezium

The perimeter of a trapezium is the total length of all four sides. To calculate the perimeter, we simply add up the lengths of each side.

Example: Let's say the trapezium has sides A = 10 cm, B = 8 cm, C = 7 cm and D = 6 cm.

Solution: The perimeter of the trapezium would be: 10 + 8 + 7 + 6 = 31

So, the perimeter of the trapezium is 31 cm.

Perimeter of a Kite

The perimeter of a kite is defined as the total length of all four sides of the kite. To calculate the Perimeter of a kite, we simply add up the lengths of the two longer sides and the two smaller sides.

Example: Consider a kite with longer sides of 20 cm and smaller sides of a length of 10 cm.

Solution: Let’s assume longer sides a and smaller side b so, perimeter of the kite:
Perimeter = 2(a + b)
Perimeter = 2(20 + 10)
Perimeter = 2 x 30
= 60 cm

Therefore, the perimeter of this kite is 60 cm.