Question

There is a pentagonal shaped park as shown in the figure.
For finding its area, Jyoti and Kavitha 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?

Answer 1

Hint: In this word problem has a pentagonal shaped park divided into two different ways for finding its area of jyoti and and kavitha then we need to find the area of park using both the way of jyoti and kavitha. Here, we recall the formula,
The area of triangle, ABE is \[\dfrac{1}{2}bh\]
The area of square, BCDE is \[{a^2}\]
Area of trapezium is \[\dfrac{1}{2}(a + b)h\]

Complete step by step solution:
Given pentagonal park is represented as follows,

The pentagonal shaped park, ABCDE has the triangle shape and the rectangle shape, we have
We know that,
The area of triangle is \[\dfrac{1}{2}bh\]
The area of square is \[{a^2}\]
Area of trapezium is \[\dfrac{1}{2}(a + b)h\]
To finding both the area of Kavita’s anf Jyothi’s way,
By calculating the way of jyoti as follows.

Area of pentagon \[ = 2\] (Area of trapezium ABCD and AFED)
 \[ = 2\left( {\dfrac{1}{2}(a + b)h} \right)\]
By substitute the values in the above formula, we get
 \[ = 2\left[ {\dfrac{1}{2}(15 + 30)\left( {\dfrac{{15}}{2}} \right)} \right] {m^2}\]
To simplify, we have
 \[ = \dfrac{{45 \times 15}}{2}{m^2} = 337.5{m^2}\]
Therefore, The area of finding of jyoti’s way if \[337.5{m^2}\]
By calculating the way of Kavitha,

Here, Area of pentagon \[ = \] Area of triangle, ABE \[ + \] Area of square BCDE

 \[ = \left[ {\left( {\dfrac{1}{2}bh} \right) + {a^2}} \right] {m^2}\]
By substitute the values in the above formula, we get
 \[ = \left[ {\left( {\dfrac{1}{2} \times 15(30 - 15)} \right) + {{\left( {15} \right)}^2}} \right] {m^2}\]
To simplify, we have
 \[ = = \left[ {112.5 + 225} \right] {m^2} = 337.5{m^2}\]
Therefore, The area of finding of kavitha’s way is \[337.5{m^2}\]

Note: Here, we need to convert the word problem into mathematical expression and find the two different ways by means of a given diagram and we remember the formula is the area of pentagon, triangle and square and trapezium to find the solution.