A horse is tied to one corner of a field which is if the shape of an equilateral triangle of side `12` m . If the length of the rope is `7`m, find the area of the field which the horse cannot graze. ( `pi = 3.14`,`sqrt 3 = 1.732`)

A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope. Find the area of that part of the field in which the horse can graze and the increase in the grazing area if the rope were 10 m long instead of 5 m.

Two charges each of magnitude 4muC are placed at two corners of an equilateral triangle of side 4m. Find the magnitude of electric field at the third corner.

A chord of a circle of radius 12cm subtends an angle of 120^@ at the center. Find the area of the corresponding segment of the circle.(use pi=3.14 and sqrt3=1.73 )

Mr. Sharma has a rectangular plot of land of length 14 m . He wants to sell a portion of it which will be of the shape of a square of side length equal to the breadth of the rectangular plot in such a manner that the remaining portion of it of the area of 50 sq. m . Is it possible?

The area of an equilateral triangle ABC is 17320.5cm^2 .With each vertex of the triangle as center,a circle is drawn with radius equal to half the length of the side of the triangle(seeFig.12.28).Find the area of the shaded region.(use pi=3.14 and sqrt3=1.73205 )

A resistance wire connected in the left gap of a metre bridge balances a 10Ω resistance in the right gap at a point which divides the bridge wire in the ratio 3:2. If the length of the resistance wire is 1.5m, then find the length of 1Ω of the resistance wire.

Length of the fence of a trapezium shaped field ABCD is 120m. If BC =48m, CD = 17m an AD=40m, find the area of this field. Side AB is perpendicualr to the parallel sides AD and BC.

Work Problem on Geometry The perimeter of a rectangular field is 80 m. If the length of the field id decreased by 2m and breadth is increased by 3 m, then the area of the field is increased by 64 sq.m. Find the dimension of the field.

There is an agriculture field in the form of rectangle of length of 20 m and width 14 m. A 10 m deep well of diameter 7 cm is dug in a corner of the field and the earth taken out of the well is spread evenly over the remaining part of the field. Find the rise in its level.