Question

Kamla has a triangular field with sides 240 m, 200 m, 360 m, where she grew

wheat. In another triangular field with sides 240 m, 320 m, 400 m 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 patatoes in one part and onions in the other part. How much area (in hectares)

has been used for wheat, potatoes and onions?​

Answer 1

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