Area of Polygon

In the fig., $\mathrm{PQRSTU}$ is a hexagon of side $5 \mathrm{cm}$ . Find the area of this hexagon using both ways.

There is a pentagonal shaped park as shown in Fig. Jyoti and Kavita divided it in two different ways .

Find the area of this park using both ways. Can you suggest some another way of finding its areas?

Find the area of the pentagonal field  $\mathrm{ABCDE}$ as shown in the fig, It is given that $\mathrm{BR}=20\mathrm{m},\mathrm{BQ}=50\mathrm{cm}, \mathrm{BP}=80\mathrm{m}, \mathrm{BE}=120\mathrm{m}, \mathrm{CR}=30\mathrm{m}, \mathrm{DP}=25\mathrm{m}$ and $\mathrm{AQ}=70\mathrm{m}$.

Suppose you have been asked to make an aeroplane from the coloured paper, as shown in figure. Find the total area of paper that you would need.

Find the area of the polygon $\mathrm{ABCDEF}$ as shown in the fig, It is given that $\mathrm{AP}=110\mathrm{m}, \mathrm{AQ}=200\mathrm{m}, \mathrm{AR}=320\mathrm{m}, \mathrm{AS}=410\mathrm{m}, \mathrm{AD}=550\mathrm{m}, \mathrm{ES}=60\mathrm{m},\mathrm{FQ}=20\mathrm{m},\mathrm{BP}=10\mathrm{m}$ and $\mathrm{CR}=50 \mathrm{m}$.

The area of a trapezium is $91 {\mathrm{cm}}^2$. and its height is $7 \mathrm{cm}$.if one of the parallel sides is longer that the other by $8 \mathrm{cm}$,find the two parallel sides.

Find the area of the figure as the sum of the areas of two trapezia and a rectangle.

The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are $1\mathrm{m}$ and $1.2\mathrm{m}$ and perpendicular distance between them is $0.8\mathrm{m}$.     

Mohan wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. If the area of this field is $10500 {\mathrm{m}}^2$and the perpendicular distance between the two parallel sides is$100 \mathrm{m}$ , find the length of the side along the river.

A trapezium with its parallel sides is in the ratio $16: 5$ is cut from a rectangular whose sides measure $63 \mathrm{m}$ and $5 \mathrm{m}$ respectively. The area of the trapezium is $\frac{4}{15}$ of the rectangle. Find the lengths of the parallel sides of the trapezium.

The shape of the cross-section of a canal is a trapezium. If the canal is $10\mathrm{m}$ wide at the top $6\mathrm{m}$ wide at the bottom and the area of its cross-section is $640 {\mathrm{m}}^2$, find the depth of the canal.

The area of a trapezium is $420 {\mathrm{m}}^2$. The perpendicular distance between the two parallel sides is $21\mathrm{m}$. If the difference of the parallel sides is $18\mathrm{m}$. Find the length of the parallel sides.

A rectangle and a square have equal area. Find out which will have the larger perimeter.

Find the area of the pentagon shown in the fig, if $\mathrm{AD}=8\mathrm{cm}$, $\text{AH=6}\mathrm{cm}$, $\mathrm{AG}=4\mathrm{cm}$, $\mathrm{AF}=3\mathrm{cm}$, $\mathrm{BF}=2\mathrm{cm}$,$\mathrm{CH}=3\mathrm{cm}$ and $\mathrm{EG}=2.5\mathrm{cm}$.