Perimeter and Area

11.1 Perimeters and Area

We learnt about the perimeters of plane figures and areas of squares and rectangles. Perimeter is the distance around a closed shaped while area is the part of plane or region occupied by the closed shaped.

Here we will learn much about the Perimeter and Area of more shapes.

11.2 Squares And Rectangles

As we learnt about the squares that's one kind of regular polygon and has four equal sides and also similar about the rectangle that has also four sides but all sides are not equals each other in this the will equal to opposite side, means One side is equal to the opposite of that side and other is equal to just opposite of that other side.

Both has the different properties, so both has different method of finding the perimeter and areas.

Perimeter of a regular polygon = number of sides x length of one side

Perimeter of a square = 4 x side

Perimeter of a rectangle = 2 x (l + b)

Area of a rectangle = l x b, Area of a square = side x side

Triangles as Parts of Rectangles

The triangle has three sides and in the triangle has to be equal and opposite side or different to be each others.

Triangle is the different kind of polygene, so this has different method of find the area and perimeter formulae.

If the triangle has equal sides of each other than-

The area of each triangle =1/2 (Area of the rectangle)

If the triangle has different sides of each other than =

The area of each triangle = 1/4 (Area of the square)

11.3 Area of A Parallelogram

Parllelogram is another type of polygone, that the similar property to the Rectangle. Similarly the Parallelogram has the length as the rectangle formed like equal to the base of the parallelogram and the breadth of the rectangle is equal to the height of the parallelogram.

Any side of a parallelogram can be chosen as base of the parallelogram. The perpendicular dropped on that side from the opposite vertex is known as height (altitude).

Yes, area of the parallelogram = area of the rectangle formed

Area of parallelogram = Area of rectangle

= length x breadth = l x b

11.4 Area of A Triangle

While we see the triangle and compare it's base and height of the triangles with the base and height of the parallelogram.

The sum of the areas of both the triangles is equal to the area of the parallelogram. The base and the height of the triangle are the same as the base and the height of the parallelogram, respectively.

Area of each triangle = 1/2 (Area of parallelogram)

= 1/2 (base x height) (Since area of a parallelogram = base x height)

=1/2(bxh) (or 1/2 bh.

All the congruent triangles are equal in area but the triangles equal in area need not be congruent.

11.5 Circles

As we know that the circle has radius with center point and the diameter that is double of the radius.

The distance around a circular region is known as its circumference.

In the circle the ratio is a constant and is denoted by Π(pi). Its approximate value is 22/7 or 3.14.

C/d = Π, where ‘C’ represents circumference of the circle and ‘d’ its diameter.

Or C = Πd

We know that diameter (d) of a circle is twice the radius (r) i.e., d = 2r

So, C = Πd = Π x 2r or C = 2Πr.

Area of the circle = Area of rectangle thus formed = l x b

= (Half of circumference) x radius

=(1/2 x 2Πr) x r

r2

So, the area of the circle = Πr2

A racing track is semi-circular at both ends.

11.6 Conversion of Units

As you know that 1 cm = 10 mm.

Many unit you will see here.

11.7 Applications

In gardens or parks, some space is left all around in the form of path or in between as cross paths. A framed picture has some space left all around it.

Such area has to called border. And the each border has the width.