1 The shaded region ABCD shows the space enclosed by two concentric
circles with centre 'O' and the angle at the centre is 75º. If the radii of
the circles are 21 cm and 42 cm, find the area of the shaded region and
the perimeter of ABCD.
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Where in the World is the Figure??!!!!
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Area of the shaded region = Area of sector OBC - Area of sector OAD
Area of sector = ∅/360° × πr²
Method I
Area of sector OBC is given by,
r = 42 cm
∅ = 75°
A = ∅/360° × πr²
= 75°/360° × 22/7 × 42²
= 1155 cm²
Area of sector OAD is given by,
r = 21 cm
∅ = 75°
A = ∅/360° × πr²
= 75°/360° × 22/7 × 21²
= 288.75 cm²
Area of the shaded region = 1155 - 288.75 = 866.25 cm²
Method II
Area of shaded portion = 75°/360° × 22/7 (42² - 21²) = 866.242 cm²
The perimeter of ABCD,
Arc length = ∅/360° × 2πr
Arc length of AD = 75°/360° × 2π × 21 = 27.5 cm
Arc length of BC = 75°/360° × 2π × 42 = 55 cm
Arc length of CD = 42 - 21 = 21 cm
Arc length of AB = CD = 21 cm
Therefore, the perimeter of ABCD = 27.5 + 55 + 21 + 21 = 124.5 cm
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