There is a pentagonal shaped park as shown in the figure. For finding its area Jyoti and Kavita divided it in two different ways.

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

Solution

Jyoti’s diagram:
The given shape is splitted into two congruent trapeziums.
Area of one trapezium = $1 half cross times left square bracket 15 plus 30 right square bracket space cross times space 15 over 2 space straight m squared$
= $1 half cross times 45 cross times 15 over 2 straight m squared$
= $675 over 4 straight m squared$
∴ Area of the pentagonal shape = $2 cross times 675 over 4 straight m squared space equals space 675 over 2 space straight m squared space equals space 337.5 space straight m squared$
Kavita's diagram:
The given shape is splitted into a square and a triangle.
Area of the square = $space space 15 space straight m space cross times space 15 space straight m space equals space 225 space straight m squared$
Area of the triangle = $1 half cross times 15 cross times 15 space equals space 225 over 2 space straight m squared space equals space 112.5 space straight m squared$
∴ Area of the pentagonal shape = $112.5 plus 225 space equals space 337.5 space straight m squared$
Another way of finding the area of the pentagonal shape:
BY splitting the pentagonal shape into 3 triangles, we have:
Area of triangle I = $1 half cross times 15 cross times 15 space straight m squared space equals space 225 over 2 space straight m squared$
Area of trianlge II = $1 half cross times 15 cross times 15 space straight m squared space equals space 225 over 2 space straight m squared$
Area of triangle III = $1 half cross times 15 cross times 15 space straight m squared space equals space 225 over 2 space straight m squared$
∴ Area of the pentagonal shape = $space 225 over 2 space straight m squared space plus space 225 over 2 space straight m squared space plus space 225 over 2 space straight m squared space equals space 337.5 space straight m squared$