4. • It is important to be able to measure and
calculate surface areas. It might be necessary
to calculate,
for example, the surface area of the cross-
section of a canal or the surface area of a
farm.
• This Section will discuss the calculation of
some of the most common surface areas: the
triangle, the square, the rectangle, the
rhombus, the parallelogram, the trapezium,
and the circle.
6. o The surface area or surface (A) of a square or a
rectangle is calculated by the formula:
A (square or rectangle) = length x width = l x w .....
(2)
In a square the lengths of all four sides are equal and
all four angles are right angles.
In a rectangle, the lengths of the opposite sides are
equal and all four angles are right angles.
SQUARES AND RECTANGLES
7. Note that in a square the length and width are equal and that in a rectangle the
length and width are not equal
8. Calculate the surface areas of the rectangle and of
the square.
Given Formula:
Square: length = 2cm
width = 2 cm
Rectangle: length = 5 cm
width = 3cm
9. Answer:
Formula: A = length x width
= 2 cm x 2 cm = 4 cm2
Formula: A = length x width
= 5 cm x 3 cm = 15 cm 2
10. Related to irrigation, you will often come across the
expression hectare (ha), which is a surface area unit. By
definition, 1 hectare equals 10 000 m2 . For example, a field
with a length of 100 m and a width of 100 m2 has a surface
area of 100 m x 100 m = 10 000 m2 = 1 ha.
11. o A volume (V) is the content of a body or
object. For example a block.
o A block has a certain length (l), width (w) and
height (h). With these three data, the volume of
the block can be calculated using the formula:
V (block) = length x width x height = l x w
x h ..... (9)
INTRODUCTION TO VOLUME
13. EXAMPLE
Calculate the volume
of the above block.
Given :
length = 4 cm
width = 3 cm
height = 2 cm
Answer:
Formula: V = length x width x height
= 4 cm x 3 cm x 2 cm
= 24 cm3
14. The volume of this block is expressed in
cubic centimeters (written as cm). Volumes
can also be expressed in cubic decimeters
(dm3), cubic meters (m3), etc.
15. Calculate the volume in m3 of a block
with a length of 4 m, a width of 50 cm
and a height of 200 mm.
Answer the ff:
Given:
All data must be converted in meters (m)
length = 4 m
width = 50 cm =
height = 200 mm =
16. 1 cm is equal to 0.01 meters
To get the equivalent of 50 cm to m, we need
to multiply it by 0.01
50 cm = 50 x 0.01 m
50 cm = 0.5 m
Therefore, 50 cm is equal to 0.5 m.
To convert millimeters to meters, divide the
unit by 1000.
200/1000 = 0.2 m
17. Calculate the volume of the same block, this
time in cubic centimeters (cm3)
Given
All data must be converted in centimeters
(cm)
length = 4 m =
width = 50 cm
height = 200 mm =
18. To convert the meter to cm, multiply the given meter
value by 100 cm.
For example, to convert 4 meters to cm, multiply 4 by 100
cm.
4 meters = 4 x 100
4 m = 400 cm
To convert the value of length in mm to cm we have to
divide the given value by 10.
200mm = 200/10 = 20 cm
