Question

please solve this question of maths ​

Answer 1

Answer:

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Area of equilateral triangle OPQ:

base = side = 10

height = 5√3

area = (1/2) × base × height = 25√3

Area of sector OPAQ:

∠POQ = 60°, so sector is 60/360 =  1/6 of circle with radius 10.

area = (1/6) × area of circle = (1/6) π r² = (1/6) π × 10² = 100π / 6 = 50π / 3

Area of semicircle PQBP:

area = (1/2) × area of circle = (1/2) π r² = (1/2) π × 5² = 25π / 2

Area of region

= (area of semicircle PQBP) - (area of sector OPAQ) + (area of triangle OPQ)

= 25 π / 2 - 50 π / 3 + 25√3

= 25 π ( 1/2 - 2/3 ) + 25√3

= 25 π ( 3/6 - 4/6 ) + 25√3

= 25 π ( -1/6 ) + 25√3

= 25 ( √3 - π / 6 )