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The length of a chain used as the boundary of a semicircular park is 108 m. Find the area of the park.
In this question the length of chain used as boundary of the semicircular park is the perimeter of the semicircular park. By using this we will first calculate the radius of the semicircular park and then area of semicircle consequently.
Length of chain = 108 m
Length of chain = Perimeter or circumference of semicircle
Therefore, Circumference or Perimeter of semicircle = 108 m
Also, Circumference or Perimeter of semicircle = πr
Where r = radius of semicircle
⇒ πr = 108
(put π = 22/7)
⇒ r = 34.46 m
Therefore, radius of semicircle is 34.36 m
As, Area of semicircle
Put value of ‘r’ in equation 1, we get
Area of semicircle
(put π = 22/7)
= 1855.63 m2
The area of the semicircular park is 1855.63 m2.
ABCD is a field in the shape of a trapezium, AD || BC, ∠ABC = 90° and ∠ADC = 60°. Four sectors are formed with centres A, B, C and D, as shown in the figure. The radius of each sector is 14 m.
Find the following:
(i) total area of the four sectors,
(ii) area of the remaining portion, given that AD = 55 m, BC = 45 m and AB = 30 m.
A child draws the figure of an aeroplane as shown. Here, the wings ABCD and FGHI are parallelograms, the tail DEF is an isosceles triangle, the cockpit CKI is a semicircle and CDFI is a square. In the given figure, BP ⊥ CD, HQ ⊥ FI and EL ⊥ DF. If CD = 8 cm, BP = HQ = 4 cm and DE = EF = 5 cm, find the area of the whole figure. [Take π = 3.14.]