A villager Ramayya has a plot of land in the shape of a quadrilateral. The grampanchayat of the village decided to take over some portion of his plot from one of the corners to construct a school. Ramayya agrees to the above proposal with the condition that he should be given equal amount of land in exchange of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented.

Open in App

Solution

$\Rightarrow$ Let ABCD is the quadrilateral plot of Rammaya.
$\Rightarrow$ Draw diagonal BD and CE\paralle$BD. Now, join DE which intersects BC at point O.
$\Rightarrow$ Now from figure,
$\Rightarrow$ $△ B D E$ and $△ B D C$ have the same base BD and between the same parallels BD and CE.
$\Rightarrow$ So, $A r e a (△ B D E) = A r e a (△ B D C)$
$\Rightarrow$ Now subtract $Area(\triangle BDO) on both sides, we get
$\Rightarrow$ $A r e a (△ B D E) - A r e a (△ B D O) = A r e a (△ B D C) - A r e a (△ B D O)$
$\Rightarrow$ $A r e a (△ C O D) = A r e a (△ B O E)$
$S o R a m m a y a c a n d i s p o s e A r e a (△ C O D) f r o m h i s p l o t A B C D a n d g e t A r e a (△ B O E) i n a d j a c e n t a n d t h e n$
$h e w i l l h a v e a t r i a n g l e l a n d A D E .$

Suggest Corrections

Similar questions

Q. A villager Ramayya has a plot of land in the shape of a quadrilateral. The gram panchayat of the village decided to take over some portion of his plat from one of the corners of construct a school. Ramayya agrees to the above proposal with the condition that he should be given equal amount of land in exchange of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented. (Draw a rough sketch of plot).

A villager Itwaari has a plot of land of the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of his plot from one of the corners to construct a Health Centre. Itwaari agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented.

Q. Question 12
A villager Itwaari has a plot of land of the shape of a quadrilateral. The Gram
Panchayat of the village decided to take over some portion of his plot from one of the corners to construct a Health Centre. Itwaari agrees to the above proposal with the condition that he should be given the equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented.

Q. A villager Itwaari has a plot of land of the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of his plot from one of the comers to construct a Health Centre. Itwaari agrees to the above proposal with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented.

Q. Question 12
A villager Itwaari has a plot of land of the shape of a quadrilateral. The Gram
Panchayat of the village decided to take over some portion of his plot from one of the corners to construct a Health Centre. Itwaari agrees to the above proposal with the condition that he should be given the equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented.

Join BYJU'S Learning Program