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A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the minor segment. [Use π = 3.14.]
Given the radius of the circle = 42 cm
Central angle of the sector = θ = 90°
Area of the minor segment = Area of sector – area of the right angle triangle
⇒ Area of the sector = 25×3.14
∴ Area of the sector = 78.5 cm2→ eqn1
∴ Area of triangle = 50 cm2→ eqn2
Area of the minor segment = 78.5 – 50 (from eqn1, eqn2)
∴ Area of the minor segment = 28.5 cm2
Area of the minor segment is 28.5 cm2.
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.]