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Side of Square Abcd is 7 Cm. with D as the Centre and Da as Radius, Arc Axc is Drawn.Find the Area of the Shaded Region with the Help of the Following Flow Chart . - Geometry

Side of square ABCD is 7 cm. With D as the centre and DA as radius, arc AXC is drawn.Find the area of the shaded region with the help of the following flow chart .

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Solution

Area of square ABCD = side2
                                   = 7 
                                   = 49 cm2
Sector D-AXC =` θ/360 `× πr2
                       = `90/360 × 22/7 × 7^2`
                       = `1/4 × 22/7 × 7 × 7`
                       = `154/4`
                       = `38.5 cm^2`
∴ Area of shaded portion = 49 - 38.5
= `10.5  cm^2`

Concept: Theorem - Converse of Tangent at Any Point to the Circle is Perpendicular to the Radius
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