Question

Please anyone help me solve all these questions from 1 to 11 . Please someone help me as I have my maths exam tomorrow . Pls guys

Answer 1

Answer:

Area of a semi circle = 1/2 πr²

Area of a semi circle = 1/2 π(5)² = 25π/2

OP = 10 cm

OQ = 10 cm (radius)

PQ = 5 + 5 = 10 cm

Since all the length are equal, it is an equilateral triangle

Area of an an equilateral triangle = √3/4 (side)²

Area = √3/4 (10)²

It is an equilateral triangle

⇒∠POQ = 60º

Area of the sector = 60/360 x π(10)²

Area = 50π/3

Find the area of the segment PAQ:

Area of the segment = Area of the sector - Area of the triangle

Area = 50π/3 - 25√3

Area = 25(2π/3 - √3)

Find the area of the shaded region:

Area = 25π/2 - 25(2π/3 - √3)

Area = 25(π/2 - 2π/3 + √3)

Area = 25( √3 - π/6) [ Shown ]