Perimeter of closed figures
Ram has a rectangular field.
The length and width of the field are
$10m$
and
$12m$
respectively.
One day, he decided to fence his field off to protect his crop from the animals.
So, he added all the sides to find the length of fencing.
The addition of all sides is called the perimeter of the shape.
And the field is a closed figure because it has the same starting point as the ending point.
Letâ€™s understand perimeter of closed figures.
The perimeter of a simple closed figure is the sum of the measures of line segments which have surrounded the figure.
Letâ€™s see how to find the perimeter of different closed shapes.
There are different closed shapes like triangle, rectangle, square, pentagons and so on.
Suppose, we have a triangle
$â–³ABC$
as,
Then, the perimeter of the triangle
$â–³ABC$
is as,
Letâ€™s take a square
$ABCD$
of side
$a$
as,
As, all the sides of the square are equal so, the perimeter of the square is as,
Letâ€™s take a rectangle
$ABCD$
of length
$l$
and width
$S$
as,
As opposite sides of the rectangle are equal so, the perimeter of the rectangle is as,
Letâ€™s see how to find the perimeter of a pentagon.
A pentagon is a closed shape which have five sides as,
So, the perimeter of the pentagon is as,
Now, suppose, we have a circle, which is also a closed figure.
The perimeter of a circle is the measure of its circumference.
Letâ€™s take a circle with center
$O$
and make a straight line from the center to the point lies on the surface of the circle.
And the distance from the center to any point on the circle is called the radius
$r$
of the circle.
The circumference of a circle can be found using the formula as,
Letâ€™ take a problem.
Suppose, we have a rectangle whose perimeter and length are
$70m$
and
$20m$
respectively.
Letâ€™s see how to find the width of the rectangle.
The perimeter of the rectangle is as,
So, the width
$b$
of the rectangle is as,
Revision
The perimeter of a simple closed figure is the sum of the measures of line segments which have surrounded the figure.
The perimeter of the different closed shapes is as,
The circumference of a circle is the perimeter of circle, can be found using the formula as,
The End