Area of Quadrilateral Using Heron's Formula

A quadrilateral whose sides are $3 \mathrm{cm}, 4 \mathrm{cm}, 4 \mathrm{cm}, 5 \mathrm{cm}$ and one of the diagonal is equal to $5 \mathrm{cm}$ as per the below figure. The area of the quadrilateral is:

Find the area of a quadrilateral $PQRS$ in which $PQ=3 cm$, $QR=4 cm$, $RS=4 cm$, $SP=5 cm$ and $PR=5 cm$.

A parallelogram has sides $6 \mathrm{cm}$ and $4 \mathrm{cm}$ and one of its diagonals is $8 \mathrm{cm}$, then its area is 

The perimeter of a rhombus is $100\mathrm{cm}$ and one of its diagonals is $48 \mathrm{cm}$. Find the length of the other diagonal.

A parallelogram has sides $24 \mathrm{cm} \mathrm{and} 16 \mathrm{cm}$. The distance between two sides of length $24 \mathrm{cm} \mathrm{is} 10 \mathrm{cm}.$ Find the distance between two sides of length $16 \mathrm{cm}.$

The perimeter of a rhombus is $20 \mathrm{cm}$. If one diagonal of the rhombus is $8 \mathrm{cm}$, find

the length of the other diagonal.

The perimeter of a rhombus is $20 \mathrm{cm}$. If one diagonal of the rhombus is $8 \mathrm{cm}$, find

the length of the other diagonal.

$\mathrm{ABCD}$ is a parallelogram and $\mathrm{P}$ is a point on $\mathrm{CD}$. If area$(△\mathrm{APC})=20 {\mathrm{cm}}^2$ and area $(△\mathrm{DPA})=15 {\mathrm{cm}}^2$:, find the area of$△\mathrm{APB}$ .

The perimeter of a rhombus is$44 \mathrm{cm}$. If the height is $10 \mathrm{cm}$, calculate its area.

The side AB of a parallelogram ABCD is of length 10cm. The diagonals AC and BD are respectively of lengths 12 cm and 16 cm. Find the area of the parallelogram ABCD.

Find the area of a rhombus whose one side is $20$ cm and one of whose diagonal is $20$ cm. 

The cost of enclosing a rectangular garden with a fence all around at the rate of $₹15$ per metre is $₹5400$. If the length of the garden is $100 \mathrm{m}$, find the area of the garden.

A house is to be constructed on a rectangular plot $40 \mathrm{m}$ long and $15 \mathrm{m}$ in the front. A minimum of $3 \mathrm{m}$, wide space has to be left in the front and back each and $2 \mathrm{m}$ wide space is to be left on each of the other sides. Find the largest area where this house can be constructed.

How many tiles $40 {\mathrm{cm}}^2$ in area will be required to pave footpath $1 \mathrm{m}$ wide carried round the outside of a grass plot $28 \mathrm{m}$ long and $18 \mathrm{m}$ wide?

In Fig. length of the field is $40 \mathrm{m}$ and breadth is $30 \mathrm{m}$. If the width of path (shaded) is $4 \mathrm{m}$, find the area of the path.

A square field has an area of $182.25 {\mathrm{m}}^2$. Find the length of a diagonal correct to the nearest metre.

A square field has an area of $182.25 {\mathrm{m}}^2$. Find the length of its side.

What is the cost of covering the floor of a corridor $100 \mathrm{m}$ long and $3 \mathrm{m}$ wide, with carpet $50 \mathrm{cm}$ wide, costing $₹15$ per metre.

In Fig. the shaded region represents the lawn in front of a house. On the three sides of the lawn, there are flower beds having a uniform width of $3.5 \mathrm{m}$. Find the area of the flower beds.

The cost of levelling a rectangular field at the rate of $85$ paise per square metre is $₹ 624.75$. Find the perimeter of the field, if its sides are in the ratio $5:3$.