a bed of roses is as shown by the shaded area in the adjoining diagram .in the centre is square of side 21 cm.if each rose plant needs 6m^2 of space ,find out the number of plants that can be planted in the whole region.
Answers
Answer:
Step-by-step explanation
Given:
Side of a square ABCD= 56 m
AC = BD (diagonals of a square are equal in length)
Diagonal of a square (AC) =√2×side of a square.
Diagonal of a square (AC) =√2 × 56 = 56√2 m.
OA= OB = 1/2AC = ½(56√2)= 28√2 m.
[Diagonals of a square bisect each other]
Let OA = OB = r m (ràdius of sector)
Area of sector OAB = (90°/360°) πr²
Area of sector OAB =(1/4)πr²
= (1/4)(22/7)(28√2)² m²
= (1/4)(22/7)(28×28 ×2) m²
= 22 × 4 × 7 ×2= 22× 56= 1232 m²
Area of sector OAB = 1232 m²
Area of ΔOAB = ½ × base ×height= 1/2×OB × OA= ½(28√2)(28√2) = ½(28×28×2)= 28×28=784 m²
Area of flower bed AB =area of sector OAB - area of ∆OAB
= 1232 - 784 = 448 m²
Area of flower bed AB = 448 m²
Similarly, area of the other flower bed CD = 448 m²
Therefore, total area = Area of square ABCD + area of flower bed AB + area of flower bed CD
=(56× 56) + 448 +448
= 3136 + 896= 4032 m²
Hence, the sum of the areas of the lawns and the flower beds are 4032 m².
HOPE THIS WILL HELP YOU...
Answer: 189
Step-by-step explanation:
The question is incorrect as the side of square is in cm but area that each plant takes is in m^2 so by the question we wont be able to grow a single plant ( as the area where plants has to grow is less than the area of one plant itself)
So i am providing solution assuming both the units are same i.e. in meters
Calculate the sum of areas of Square and 4 semicircles on its side
Area of Square = 21x21 = 441 m^2
Area of 4 semi circles = 4x 1/2 x 22/7 x 21/2 x 21/2 = 693 m^2 ( The radius of each semicircle will be Side of the square divided by 2)
Sum of the areas = 441+ 693 = 1134m^2
Now to get the number of rose plants divide the area taken by each rose plant i.e. 6m^2 to the total area i.e 1134m^2
So 1134/6 = 189 rose plants