Kamia has a triangular field with sides 240m, 200m, 360m, where she grew wheat. In
another triangular field with sides 240m, 320m, 400m adjacent to the previous field, she
wanted to grow potatoes and onions. She divided the field in two parts by joining the mid-
point of the longest side to the opposite vertex and grew potatoes in one part and onions
in the other Part. How much area has been used for wheat potatoes and onijons?
(1 hectare = 10,000 m2)
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
Step-by-step explanation:
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