Question

A surveyor has produced this plan of property. Find its area

Answer 1

4300 m²

1) As this is not a regular pentagon for their lengths are not congruent to each other let's decompose that pentagon into other polygons:

So we have a quadrilateral below and a triangle on top.

Area of that triangle below:

`A=(1)/(2)\cdot b\cdot h\rightarrow A=100*60*(1)/(2)=300m^2`

Considering that quadrilateral is a parallelogram with two pairs of parallel and congruent sides

`\begin{gathered} A=w\cdot l \\ A=80*50 \\ A=4000m^2 \end{gathered}`

The area of that pentagon:

`A=4000+300,A=4300m^2`