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 |
|
=1/2*70*60 |
2100 |
|
|
2 |
|
=1/2*15*80 |
600 |
|
|
3 |
Trapezium
FRGQ |
=1/2*(60+15)*20 |
750 |
|
|
4 |
Trapezium
SCPB |
=1/2*(20+70)*65 |
2925 |
|
|
5 |
|
=1/2*20*100 |
1000 |
|
|
6 |
Trapezium
ETRF |
=1/2*(90+60)*75
|
5625 |
|
|
7 |
|
=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. |
PBA