An equilateral triangle has all three sides equal and and all three angles equal to 60° The relationship between the side \( a \) of the equilateral triangle and its area A, height h, radius R of the circumscribed and radius r of the inscribed circle are give by:
Area A = \( a^2\dfrac{\sqrt 3}{4} \)
h = \( a\dfrac{\sqrt 3}{2} \)
R = \( a\dfrac{\sqrt 3}{3} \)
r = \( a\dfrac{\sqrt 3}{6} \)
Problems with Solutions

What is the area of an equilateral triangle of perimeter 45 cm?

What is the area of an equilateral triangle of height 20 units?

What is the area of the circumscribed circle of an equilateral triangle of side a = 5 inches?

What is the radius of the inscribed circle of an equilateral triangle with an area of 100 cm^{ 2}?

What is the ratio of the area of the circumscribed circle to the area of the inscribed circle of an equilateral triangle?

What is the area of triangle CA'B' if ABC is an equilateral triangle and A'B' is parallel to AB?

What is is the area of the shaded (in green) shape shown below if ABC is an equilateral triangle of side a = 10 has an inscribed circle, with center O, and is tangent at P and M to the sides AC and AB respectively?

Find the coordinates of point C such that triangle ABC is equilateral of side 12 units.

What is the area of the triangle BB'B" if ABC is an equilateral triangle of side 10 units and A'B' is parallel to AB?

What is the area of the shaded shape (in red) if all three circles have equal radii of 15 units and are tangent to each other?