6.16 Scale
(Surveyors) Drawing.
You must have observed that lands of farmers are
not in exact shapes of Triangles or rectangles or trapeziums or parallelograms.
Still, we need to measure the area of lands.
Similar is the case when we need to calculate the area of forests or catchments
areas of rivers.
Surveyors are the people appointed by Government
and other agencies who measure the area of the
irregular sized polygon and calculate
their areas for planning purposes.
Since fields and rivers have dimensions in kilo meters we use a suitable scale
to draw their figures on paper
(For example 1cm = 1meter, 1cm = 100 kilo meters..).
We know how to calculate the areas of:
No. 
Object 
Area 
Explanation 
1 
Triangle 
(1/2)bh 
B
is the base and h is the height 
2 
Rectangle 
lb 
l
is length and b is breadth 
3 
Trapezium 
(1/2)(a+b)h 
a
and b are lengths of parallel sides, h
is the height 
6.16 Problem 1: Calculate the area of the below mentioned figure
and represent the data in the table as recorded by surveyors
Method:
Step 
Procedure 
1 
Irregular
shaped field is divided in to geometrical shaped objects such as triangles,
rectangles, and trapezium 
5 
Use
suitable scale to draw figures on sheet of paper 
4 
Calculate
the areas of individual geometrical shaped objects 
5 
Multiply
the figure by the scales to arrive at actual area 
The adjoining figure is represented by surveyors as
follows
No. 
In meters to Points( on left
side of AD) 
In meters to points 
In meters to Points( on right side of AD) 
1 

From A to P 60 
From P to B 70 
2 
From Q to G 15 
From A to Q 80 

3 
From R to F 60 
From A to R 100 

4 

From A to S 125 
From S to C 20 
5 
From T to E 90 
From A to T 175 

6 

From A to D 225 

Calculation of areas of different figures: (For
drawing the figure, we have used a scale: 1cm = 10 Meter)
No. 
Areas of 
As per formula 
= in Sq meters 

1 
_{}PBA 
=1/2*70*60 
2100 

2 
_{}GQA 
=1/2*15*80 
600 

3 
Trapezium
FRGQ 
=1/2*(60+15)*20 
750 

4 
Trapezium
SCPB 
=1/2*(20+70)*65 
2925 

5 
_{}DSC 
=1/2*20*100 
1000 

6 
Trapezium
ETRF 
=1/2*(90+60)*75

5625 

7 
_{}ETD 
=1/2*90*50 
2250 



Total area 
15250 
6.16 Summary of learning
No 
Points learnt 
1 
Convert
Surveyor’s drawing into shapes of triangles, rectangles and trapezium 
2 
Use
suitable scale and formulae to calculate the area. 