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geometry

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137
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Semi circles are constructed on the three sides of a triangle as shown below. Find the area of the shaded region Jun 27, 2021

#1
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12 and 5 are the diameters of the two circles of the legs of the triangle

find hypotenuse by pythagorean theorem    h^2  = 12^2 + 5^2       h = 13 = diameter of third semi circle

the radii of the semi circles are   6   2.5   and   6.5

Area of a full circle = pi r^2         area of semi circle = 1/2 pi r^2

add all of the semi circle areas together       1/2 pi ( 6^2 + 2.5^2 + 6.5^2 )  = ___________ units2

Jun 27, 2021

#1
+2

12 and 5 are the diameters of the two circles of the legs of the triangle

find hypotenuse by pythagorean theorem    h^2  = 12^2 + 5^2       h = 13 = diameter of third semi circle

the radii of the semi circles are   6   2.5   and   6.5

Area of a full circle = pi r^2         area of semi circle = 1/2 pi r^2

add all of the semi circle areas together       1/2 pi ( 6^2 + 2.5^2 + 6.5^2 )  = ___________ units2

ElectricPavlov Jun 27, 2021