Question : The parallel sides of a trapezium are $8\;\mathrm{cm}$ and $4\;\mathrm{cm}$. If the $\mathrm{M}$ and $\mathrm{N}$ are the mid-points of the diagonals of the trapezium, then the length of $\mathrm{MN}$ is:

Question : If $\mathrm{D}$ is the midpoint of $\mathrm{BC}$ in $\triangle \mathrm{ABC}$ and $\angle A=90^{\circ}$, then $AD=$ ______.

Question : The area of an isosceles trapezium is 176 cm² and the height is $\frac{2}{11}$th of the sum of its parallel sides. If the ratio of the length of the parallel sides is 4 : 7, then the length of a diagonal (in cm) is:

Question : ABCD is a cyclic quadrilateral. Sides AB and DC, when produced, meet at E and sides AD and BC, meet at F. If $\angle $ADC = 76$^\circ$ and $\angle$AED = 55$^\circ$, then $\angle$AFB is equal to:

Question : In a trapezium ABCD, AB and DC are parallel to each other with a perpendicular distance of 8 m between them. Also, AD = BC = 10 m, and AB = 15 m < DC. What is the perimeter (in m) of the trapezium ABCD?