Maharashtra Board Solutions for Chapter: Quadrilaterals, Exercise 6: Problem set 5

If all pairs of adjacent sides of a quadrilateral are congruent then it is called

If the diagonal of a square is $12\sqrt{2} \mathrm{cm}$ then the perimeter of square is 

If opposite angles of a rhombus are $\left(2x\right)°$ and $\left(3x-40\right)°$, then the value of $x$ is

Adjacent sides of a rectangle are $7 \mathrm{cm}$ and $24 \mathrm{cm}$. If the length of its diagonal is $k \mathrm{cm}$, then find the value of $k$. 

If diagonal of a square is $13$ $cm$ then if its side is $k cm$ then find the value of $k$.

Write your answer up to three decimal places.

Diagonals PR and QS of a rhombus PQRS are $20$ $cm$ and $48 cm$ respectively. Find the length of side PQ.

Diagonals of a rectangle PQRS are intersecting in point M. If $\angle QMR=50°$ then the measure of $\angle MPS$ is $k°$. Find the value of $k$.

In the adjacent figure, $\square ABCD$ is a trapezium. $AB\parallel DC$. Points $M$ and $N$ are midpoints of diagonal $AC$ and $DB$ respectively then prove that $MN\parallel AB$.