Question

28. A farmer has two pieces of land in a parallelogram shape on the same base. He grows
vegetables and flowers in two triangular pieces of land as shown in diagram:
(1) Check whether the two triangular pieces of land are equal in areas.
(i) What values are being displayed by the farmer?
​

Answer 1

Yes ,  two triangular pieces of land are equal in areas

Step-by-step explanation:

Let draw AM ⊥ FE    &  BN ⊥CD

 AB ║ EF ║ CD

& EF are CD on same line

=> AM = BN

AB = EF

AB = CD

=> CD = FE

FD = EF - DE =  AB - DE

CE = CD - DE = AB - DE

=> FD = CE  

Area of Δ ADF = (1/2) FD * AM

Area of ΔBCE = ( 1/2) CE * BN

FD = CE    & AM = BN

=> Area of Δ ADF = Area of ΔBCE

Yes ,  two triangular pieces of land are equal in areas

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Answer 2

YES , area of two triangular pieces of land are equal

Step-by-step explanation:

given :A farmer has two pieces of land in a parallelogram shape on the same base. He grows  vegetables and flowers in two triangular pieces of land

Let draw AM ⊥ FE    &  BN ⊥CD

AB ║ EF ║ CD   & EF and CD are  on the same line

AM = BN

AB = EF

AB = CD  

CD = FE

now ,

FD = EF - DE =  AB - DE

CE = CD - DE = AB - DE

 FD = CE  

therefore ,

Area of Δ ADF = Area of ΔBCE

hence , Yes ,  two triangular pieces of land are equal in areas

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