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:
Visually the pentagon is divided into two equal trapeziums or into one triangle and one square as per Jyothi's and Kavita's approach.
(i) Jyoti’s way of finding the area is as follows:
Area of pentagon ABCDE = Area of trapezium ABCF + Area of trapezium AEDF
= 1/2 × (AF + BC) × FC + 1/2 × (AF + ED) × DF
= 1/2 × (30 m + 15 m) × 15/2 m + 1/2 × (30 + 15 m) × 15/2 m
= 2 × 1/2 (30 m + 15 m) × 15/2
= 45 m × 7.5 m
= 337.5 m²
Thus, the area of the pentagonal shaped park according to Jyoti’s way is 337.5 m²
(ii) Kavitha’s way of finding the area is as follows:
Area of pentagon ABCDE = Area of triangle ABE + Area of square EBCD
= 1/2 × BE × (AF − OF) + FC × BC [Since, AO = AF - OF]
= 1/2 × 15 × (30 − 15) + (15 × 15 )
= (1/2 × 15 × 15) m² + 225 m²
= 112.5 m² + 225 m²
= 337.5 m²
Thus, the area of the pentagonal shaped park according to Kavitha’s way is 337.5 m²
Another way of finding its area is as follows.
By symmetry, Area of ΔAFB = Area of ΔCGB
Also, B is the mid point of FG. Thus, FB = BG = 7.5 m
GC = AF = 30 - 15 = 15 m
Area of pentagon ABCDE = Area of rectangle GFED – (Area of ΔAFB + Area of ΔCGB)
= GD × ED - 2 × [1/2 × FB × AF]
= 30 m × 15 m − 2 × [1/2 × 7.5 × 15]
= 450 m² - 112.5 m²
= 337.5 m²
☛ Check: NCERT Solutions for Class 8 Maths Chapter 11
Video Solution:
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?
Class 8 Maths NCERT Solutions Chapter 11 Exercise 11.2 Question 10
Summary:
There is a pentagonal shaped park as shown in the figure. For finding its area Jyoti and Kavita divided it in two different ways. The area of the pentagonal shaped park according to Jyoti’s and Kavitha’s way is 337.5 m².
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