Area of a Polygon

The diagonal of a quadrilateral-shaped field is $12 \mathrm{m}$ and the perpendiculars dropped on it from the remaining opposite vertices are $6 \mathrm{m}$ and $8 \mathrm{m}$. Find the area of the field by the method of triangulation.

Find the area of the regular pentagon given below by the method of triangulation.

Find the area of the below polygon by the method of triangulation.

In the Fig, $ABCD$ is a trapezium in which $AB\left|\right|DC, AFCD$ is a parallelogram, $BFC$ is a triangle. Area of $△BFC=48 {\mathrm{cm}}^2, FB=16 \mathrm{cm}$ and $DC=13 \mathrm{cm}$. Find the area of the trapezium $ABCD$(excluding units) .

Find the area of the field (excluding units) as shown in the Fig. All dimensions are in $\mathrm{m}$.

Find the area of the field (excluding units) as shown in the Fig. All diameters are in $\mathrm{m}$.

Find the area of the polygon $PQRST$ (excluding units) given in the figure, given that all measurements are in $\mathrm{cm}$.

Find the area of the polygon $ABCDE$ (excluding units), if $AD=16 \mathrm{cm},\mathit{ }AH=12 \mathrm{cm}, AG=8 \mathrm{cm}, AF=6 \mathrm{cm}$ and perpendiculars $BF=4 \mathrm{cm}, CH=6 \mathrm{cm}$ and $EG=2.5 \mathrm{cm}$

Determine the area of the pentagonal (excluding units) field shown in the figure. All dimensions are in metres.

Find the area of the field (excluding units) as shown in the figure. All dimensions are in $\mathrm{m}$.

Area of a polygon is

If the area of an equilateral triangle of side $20 \mathrm{m}$ is $A {\mathrm{m}}^2$, then find the value of $A$. [Assume $\sqrt{3}=1.732$]

If the area of the following figure is $\frac{p\sqrt{q}}{2} {\mathrm{m}}^2$ then, find the value of $p+q$.