Surface Measurement


Perimeter and Area - 2


Dear friend,

you must have noticed in the previous section that

by adding more lines or by bending the line

we can cover some area.


Thus we added one more dimension.


By adding one more dimension we made different shapes or two dimensional figures.


Two dimensional geometric figures now have Surface Area.


The surface area of any figure (two dimensional or three dimensional) is

the sum of all the areas of all the shapes that cover the surface of the object.


Surface area is measured in Square Units.


You have to keep in mind that while calculating the surface area you have to use the same units for all the measurements.

For example, you can not use inches for length and centimeters for the width.


There are different equations for different geometric figures to find out their surface area.


For example:


For square you multiply length x 4 = its surface area in square units.

For triangle you multiply length of its base x its height = its surface area in square units.

For Rectangle you multiply its length x its width = its surface area in square units.

For circle the equation is pi x r, where Pi is a constant. Pi = 3.141592... and r is radius of the circle.



The distance around a figure is called its perimeter.


This is equal to the sum of its all sides.


Now let us see some of the equations for surface areas for some common geometric figures.



 surface area = a x a = a, perimeter = a + a + a + a

      = 4 x a

 = 4a



surface area = a x b = ab,

perimeter = a + b + a + b

           = 2a + 2b

           = 2(a + b)






surface area = b x h = bh, perimeter = a + b + a + b = 2a + 2b = 2(a + b)


surface area = h/2 + (b1 + b2), perimeter = a1 + b1 + a2 + b 2


surface area = pi r x r = pi r, perimeter = pi x 2r

                = pi x d

Circle   where d is diameter of the circle


surface area = pi x r1 x r2

                      = pi r1r2,

perimeter there is no simple exact formula
Ellipse   Some formulas are simple but not exact, while some formulas are exact but not simple


surface area = 1/2 x (b x h) = 1/2 (bh) perimeter = a + b + c


Surface area of a regular polygon = (1/2) x n x sin(360/n) x s,

where n = number of sides,

s = length from center to a corner


Table of Surface Measure


Traditional System


144 square inches = 1 sq. ft.

9 square feet = 1 sq. yard

30 1/4 sq. yds. = 1 sq. rod

160 sq. rods.  = 1 acre

640 acres = 1 sq. mile

1 acre = 208.71 ft. x 208.71 ft.


Table of Surface Measure


Metric System


meter x 10 = decameter

meter x  100 = hectometer

meter x 1000 = kilometer



Conversion between metric and customary systems


From multiply by To get
square feet 0.0929 square meters
square yards 0.8361 square meters
square miles 2.59 square kilometers
From multiply by To get
square kilometers 0.3861 square miles
hectares 2.4710 acres