Area of a General Quadrilateral

The Diagonal $AC=15 cm$ of $ABCD$ and the lengths of the perpendiculars drawn from $B$ and $D$ to $AC$ are $3 cm$ and $5 cm$ respectively. Then find the area of the quadrilateral $ABCD$. 

Area of a rhombus $=\frac{1}{2}\times$ product of _____

The area of a rhombus is $2016 {\mathrm{cm}}^2$ and its sides are $65 \mathrm{cm}$ each. Find the lengths of its diagonals.

Shown below is rhombus $\mathrm{ABCD}.$

Its diagonals, $\mathrm{AC} = 24 \mathrm{cm}$ and $\mathrm{BD} = 10 \mathrm{cm},$

What is the length of its side $\mathrm{CD}$?

A goldsmith took the measurements around a Ruby stone and found it to be 12cm. What is this measurement?

Raju drew a Rhombus of side ‘a’ cm. His teacher told him to increase the side to 4 less than twice the current size. What will be the perimeter of the new rhombus?

The diagonals of a rhombus are $12 \mathrm{cm}$ and $15 \mathrm{cm}$. The area of the rhombus is equal to

If the area of the parallelogram with base $=60 \mathrm{cm}$ and height $=30 \mathrm{cm}$ is $\mathrm{k} {\mathrm{cm}}^2$, then find $\mathrm{k}$.

If the diagonal $d$ of a quadrilateral is doubled and the heights $h_1$ and $h_2$ falling on $d$ are halved, then the area of quadrilateral _____.

The area of a rhombus whose diagonals are $10 \mathrm{cm}$ and $20 \mathrm{cm}$ is equal to
 

An auditorium hall is in the shape of a rhombus such that the lengths of the two diagonals of the hall are $12 \mathrm{m}$ and $16 \mathrm{m}$. Find the cost of painting the floor at the rate of $₹ 6.50 \mathrm{per} \mathrm{sq}. \mathrm{m}$.

The length of a diagonal of a quadrilateral shaped field is $48 \mathrm{m}$ and the lengths of perpendiculars dropped on it from the remaining opposite vertices are $16 \mathrm{m}$ and $26 \mathrm{m}$. Find the area of the field.

If the lengths of two diagonals of a rhombus are $16 \mathrm{cm}$ and $30 \mathrm{cm}$, find the area and the length of the side of the rhombus.

To tile the floor of a room of dimensions $8 \mathrm{m} \times 4·8 \mathrm{m},$ rhombus-shaped tiles of diagonals $16 \mathrm{cm}$ and $12 \mathrm{cm}$ costing $₹24$ and square-shaped tiles of diagonal $16 \mathrm{cm}$ costing $₹28$ are available. Which type of tiles should be chosen to minimize the cost? How much can be saved by choosing the right type over the other?