What is the area of the shaded portion, Equilateral Triangle side is 6cm and circle radius is 1.5cm
Answers
Answer:
The triangle is circumscribed by a circle right?
Well for a triangle having side lengths a,b and c the circumradius R can be given by the formula -
R= abc/4∆
where ∆ is the area of the triangle.
(For a proof of the above equation, ask me in comments)
For equilateral triangle,
a=b=c= l (let)
∆ = √3l^2/4
=> l=√(4∆/√3) - i
R = l^3/4∆
=> l = (4∆R)^1/3 - ii
equating i and ii and raising both sides to the power 6 , we get
64∆^3/3√3 = 16∆^2R^2
=> ∆ = 3√3R^2/4
Plugging in the value of R = 10 cm
∆ = 129.90 cm^2
Hope that helps!
Answer:
Step-by-step explanation:
The triangle is circumscribed by a circle right?
Well for a triangle having side lengths a,b and c the circumradius R can be given by the formula -
R= abc/4∆
where ∆ is the area of the triangle.
(For a proof of the above equation, ask me in comments)
For equilateral triangle,
a=b=c= l (let)
∆ = √3l^2/4
=> l=√(4∆/√3) - i
R = l^3/4∆
=> l = (4∆R)^1/3 - ii
equating i and ii and raising both sides to the power 6 , we get
64∆^3/3√3 = 16∆^2R^2
=> ∆ = 3√3R^2/4
Plugging in the value of R = 10 cm
∆ = 129.90 cm^2