Given:$ABCD$ is a parallelogram, $AE \perp DC$ and $CF \perp AD$.$AB = 16\ cm, AE = 8\ cm$ and $CF = 10\ cm$.To do:We have to find $AD$.Solution:We know that, Area of a parallelogram $=$ Base $\times$ AltitudeTherefore, Area of parallelogram $ABCD = AB \times AE$$= 16 \times 8$$= 128\ ... Read More

To do:We have to find whether the given figures lie on the same base and between the same parallels and write the common base and two parallels.Solution:(i) From the figure, Trapezium $ABCD$ and triangle $DPC$ on the same base $DC$ and between the same parallels $AB$ and $DC$ . (ii) From ... Read More

Given:hexagonal and star shaped rangolies.To do:We have to fill the given rangolies with as many equilateral triangles of side $1\ cm$ as we can and count the number of triangles in each case, which has more triangles.Solution:Let us calculate the area of hexagon and star, Area of hexagon$= 6\times\frac{25\sqrt 3}{4}$Area ... Read More

Given:In a huge park, people are concentrated at three points.To do:We have to find where to set up an icecream parlour so that maximum number of persons can approach.Solution:Let us consider $ABC$ as a triangle.Such that the three points in a triangle will be equidistant at circumcentre from the points ... Read More

To do:In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.Solution:Let us consider a $\triangle ABC$We know that, A point in the interior of the triangle, equidistant from all the sides of the triangle will be its Incenter.The incenter of a ... Read More

Given: $ABC$ is a triangle.To do:We have to locate a point in the interior of $\triangle ABC$ which is equidistant from all the vertices of $\triangle ABC$.Solution:Let us consider a $\triangle ABC$We know that, A point in the interior of the triangle which is equidistant from all the vertices is called ... Read More

To do:We have to show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.Solution:Let us draw a line $l$ and mark a point $P$ on it.Now let us draw a perpendicular line $AB$ on $l$ and let us point ... Read More

Given:$PR > PQ$ and $PS$ bisects $\angle QPR$.To do:We have to prove that $\angle PSR > \angle PSQ$.Solution:Let us consider $\triangle PQR$We have, $PR > PQ$We know that, The angle opposite the longer side will always be larger.This implies, $\angle PQR > \angle PRQ$...(i)Since we have, $PS$ bisects $\angle QPR$We ... Read More

Given:$AB$ and $CD$ are respectively the smallest and longest sides of a quadrilateral $ABCD$.To do:We have to show that $\angle A>\angle C$ and $\angle B>\angle $D$.Solution:Let us consider $\triangle ABD$, We have, $AB We know that, The angle opposite the longer side will always be larger.This implies, $\angle ADB In ... Read More

Given:$\angle B