0. The sides of a triangular field are 320 m, 200 m and 180 m long. Using ruler and compasses only, draw the plan of the field using the scale 50 m=1 cm. Construct the altitude of the triangle on the side representing 320 m. Measure the altitude and use your result to calculate the area of the actual field in m². (ICSE)
Answers
Answer:
E is the midpoint of AD, then
AE=ED=200m
Area of wheat field =ar△ABC
Area of potato field =ar△AEC
Area of onion field =ar△EDC
ar△ABC =
S(S−a)(S−b)(S−c)
,S=
2
200+240+360
=400m
=
400(400−200)(400−240)(400−360)
=
400×200×160×40
=16000
2
m
2
=1.6
2
hectare
=1.6×1.414=2.26hectares
In △ACD
△AEC and △CED have same base [arAE=ED=200m]
and they have same height CF
Therefore, ar△AEC=ar△CED=
2
1
ar△ACD
ar△ACD =
S(S−a)(S−b)(S−c)
,S=
2
240+320+400
=480m
=
480(480−240)(480−320)(480−400)
=
480×240×160×80
=38400m
2
=3.84hectares
∴ar△AEC=ar△CED=
2
1
×3.84=1.92hectares
Therefore,
Area of wheat field =2.26hectares
Area of potato field =1.92hectares
Area of onion field =1.92hectares
For potato 100m=100×1.92=192hectares