Question

Calculate the height of an equilateral triangle which has the same area as a circle with a circumference of 10cm.

Give your answer correct to 3 significant figures.

Answer 1

Area of the Circle= 2π R
= 2×22/7×10
= 440/7 sq cm
Area of Equilateral Triangle =√3/ 4 × a ^2
440/7 = √3/4 × a^2
( 440× 4) / (7√3) = a^2
a^2 =145.17 sq cm
a =12.05 cm
All sides of equilateral triangle are equal = 12.05 cm
If we draw a perpendicular from the vertex, it will devide the triangle in to two equal right angled triangles.
A right angled triangle will have hypotenuse of 22.05 cm and a side of 12.05/2 = 6.025 cm
applying Pythagoras theorem
(height)^2= √( 12.05)^2 --(6.025)^2
height =10.44 cm