Perimeter

Mensuration

As cultures advanced, human beings constructed various shapes which were geometrical. Their fields were rectangular or triangular, their wells were cylindrical, houses were cones or cubes etc. Their farm produce was stored in containers. They needed to measure areas, volumes of these shapes possibly for purpose of deciding the tax payable. They also needed to construct these shapes to certain measurements. Hence they combined their knowledge of geometrical shapes with their understanding of principles of measurement. The discipline of “mensuration” developed as an independent topic.

Three of the geometrical properties they had to understand were perimeter, area (plane & curved) & volume. We will see each of these in subsequent chapters.

Perimeter

Perimeter is the total length of a line enclosing a figure. It can be thought of as the length of a fence around a field or a compound enclosing a house.

We give below the perimeter of a few commonly used figures.

Triangle – If we call the lengths of the three sides of a triangle as a, b, & c, then the perimeter of the triangle would be P= a + b + c.

Rectangle– If 2 adjacent sides of a rectangle are a & b, the other 2 sides would also be a & b and hence the perimeter of a rectangle would be P = 2a + 2b = 2(a + b)

Square– In a square all the sides are equal. So the perimeter would be 4a, where a is the length of the sides of the square.

Circle– the perimeter of a circle has a special name – circumference. This is possibly because the perimeter of a circle was studied for many centuries. IT was found to be related to a special number which is written as π and is pronounced as “pie”.

π is a very important number in mathematics. It has a very rich history which we will study in chapter 32.2.

The circumference of a circle was found to be πd or 2πr, where d is the diameter of the circle and r is its radius.

Perimeter of complex figures

In real life we will come across figures which are made of different kinds of simple figures. For example there could be a rectangular lawn with a circular patch on one of the sides.

Perimeters of such figures can be found in the following way. First the complex figure is divided into a series of simple figures. Then the part of the perimeter of each figure, which would be part of the perimeter of the entire figure can be worked out. The individual perimeter portions can be added to give the perimeter of the entire figure.

Chapter 25.3 gives some activities for understanding the inter-related properties of area & perimeter.