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 = $$\frac{2}{3}\times\ h$$

▪ 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

Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and Y, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of X is more than that of Y, the ratio of the radii of X and Y is

Question 3

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

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