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Start with a square and draw a circle around it. Divide the square in half on the diagonal If the side of the square is 5, what is the diagonal A 2 + B 2 = C 2 5 2 + 5 2 = C 2 50 = C 2 √ 50 = √C 2 = C √2 x √25 = C √2 x 5 = 5√2 = C What’s the green shaded area?.
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Start with a square and draw a circle around it. Divide the square in half on the diagonal If the side of the square is 5, what is the diagonal A2 + B2 = C2 52 + 52 = C2 50 = C2 √ 50 = √C2 = C √2 x √25 = C √2 x 5 = 5√2 = C What’s the green shaded area? AC = πr2 As = s2 Cc= πD = 2πr Square in a Circle 5√ 2 5
What’s the green shaded area? First of all the green shaded area is the area of the circle minus the area of the square. Area of the square is 5 x 5= 25 Area of the circle is πr2 r = ½ 5√2 = π(5/2√2)2 What !! Don’t panic 5/2 x 5/2 x √2 x √2= 25/4 x 2 = 50/4 = 25/2 Ac= π25/2 Green area= π25/2- 25 Green area= 25(π/2- 1) AC = πr2 As = s2 Cc= πD = 2πr Square in a circle 5 5√ 2
Area of circle – Area of Square π r2 - s2 If the diagonal = 10 (r = 5) Shade = 25π - 5√2 x 5√2 Shade = 25π - 50 Shade = 25(π–2) If the side = 10 Shade = π(5√2 x 5√2) – 10 x 10 Shade = 50π - 100 Shade = 50(π-2) . Square in a Circle
Area of square- Area of circle s2 = πr2 If the side =10, radius = 5 (1/2D) 10 x 10 - π 52 100 - 25π = 25(4= π) Don’t be fooled . Circle in a Square
