Rampur sarpanch requested one of his villager to donate a 6m wide land adjusted to his 132.8m long side of his right triangular plot outside the village . the other sides of the plot is 123m and 50m .on his donated land , the sarpanch wants to construct a link road which provides the connectivity with the other villages and towns . the villager agreed at once . i) find the area of the triangular plot remaining with the villager . ii) what are the values involved here ?

Area of the remaining triangle with the villager is 1243.13 m²

Step-by-step explanation:

Triangle ABC is the triangular plot of a villager shown in the figure attached.

Sarpanch requested the villager to donate land which is 6 m wide and along the side AC which measures 132.8m.

Other sides of the plot has been given as AB = 50m and BC = 123 m.

Now area of this land before donation =

=

= 3075 square meter

After donation of the land the triangle formed is ΔDBE.

In ΔABC,

tan(∠ABC) =

                 = 0.4065

∠ABC =

          = 22.12°

In ΔEFC,

tanC =

0.4065 =

CF =

CF = 14.76 m

Since DE = AC - (CF + AG)

               = 132.8 - (2×14.76)

               = 132.8 - 29.52

               = 102.48 m

Now in ΔDBE,

sin(∠DEB) =

sin(22.12) =

DB = 102.48×0.3765

     = 38.59 m

Similarly, cos(22.12) =

0.9264 =

BE = 102.48×0.9264

     = 94.94m

Now area of ΔDBE =

                                =

                                = 1831.87 square meter

Area of remaining triangle with the villager = Area of ΔABC - Area of ΔDBE

= 3075 - 1831.87

= 1243.13 square meter

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