Triangles - Area of types of triangles

Rarely Tested

If x is the side of an equilateral triangle, then the

Altitude (h) =$$\frac{\sqrt{\ 3}}{2}x$$

Area =$$\frac{\sqrt{\ 3}}{4}x^2$$

Inradius = $$\frac{1}{3}\times\ h$$

Circumradius = $$\frac{2}{3}\times\ h$$

β–ͺ Area of an isosceles triangle =$$\frac{a}{4}\sqrt{\ 4c^2-a^2}$$ (where a, b and c are the lengths of the sides of BC, AC and AB, respectively, b = c).

Question 1

If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is

Question 2

What is the least possible perimeter of a triangle whose area is 144$$\sqrt{3}$$ sq cm?

Question 3

An equilateral triangle and a square are inscribed in a circle. What is the ratio of the area of the triangle to the ratio of the square?

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