Manipur Board Solutions for Chapter: Area, Exercise 1: EXERCISE 9.1

Prove that the line segment joining the midpoints of a pair of opposite sides of a parallelogram divides it into two parallelograms of equal area.

Prove that three parallelograms formed by joining the midpoints of the three sides of a triangle are equal in area.

Prove that, of all the parallelogram of given sides, parallelogram which is a rectangle has the greatest area.

If $O$ is an interior point of a parallelogram $ABCD$, prove that area of $△AOB+$ area of $△OCD=\frac{1}{2}$area of parallelogram $ABCD$.

If $O$ is an interior point of a parallelogram $ABCD$, prove that area of $△AOB+$ area of $△OCD=$area of $△OAB+$area of $△OCD$

$ABCD$ is a parallelogram and $P$ is any point on the side $CD$. Prove that area of $△APD+$area of $△BCP=$area of $△ABP$.

$ABCD$ and $ABPQ$ are parallelogram such that the points $C, D, P, Q$ are collinear and $R$ is any point on the side $BP$. Show that area of parallelogram $ABCD=$area of parallelogram $ABPQ$.

$ABCD$ and $ABPQ$ are parallelogram such that the points $C, D, P, Q$ are collinear and $R$ is any point on the side BP. Show that area of $△ARQ=\frac{1}{2}$area of parallelogram $ABCD$.