Q 10. 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?
find its own way
will be the brainlist
Answers
Answer:
==========================================================
Solution;
By Jyoti’s diagram:
Area of Trapezium= ½ × (Sum of parallel sides) × Perpendicular distance
Area of pentagon = Area of trapezium ABCP + Area of trapezium AEDP
= ½ (AP + BC) x CP + ½ (ED + AP) x DP
=½ (30 + 15 ) x CP + ½ (15 + 30) xDP
= ½ (30 + 15) (CP + DP)
= ½ X 45 x CD [CP + DP = CD]
= ½ x 45 x 15 =337.5 m²
Area of pentagon =337.5 m²
By Kavita’s diagram
A perpendicular is drawn from the vertex of a triangle to the base of a triangle. height of a triangle = 30 - 15 = 15 m & base =15 m
Area of Triangle= ½ x base x height
Area of square = side x side
Area of pentagon
= Area of triangle ABE + Area of square BCDE
=½ x15 x 15+(15 x15) = ½ x 225 + 225
= 112.5 + 225.0
= 337.5 m²
Hence total area of pentagon shaped park = 337.5 m²
=========================================================
Hope it helps!