Answer:
18[tex]\sqrt{3}[/tex]
Step-by-step explanation:
altitude h=[tex]\frac{\sqrt{3}*a }{2}[/tex], where a equals the length of one side
6=[tex]\frac{\sqrt{3}*a }{2}[/tex]
a=[tex]\frac{2*6}{\sqrt{3} }[/tex]
a=[tex]\frac{2*\sqrt{3} *\sqrt{3} *3}{\sqrt{3} }[/tex]
Area of a triangle=[tex]\frac{1}{2} *base *height[/tex]
base=a
a=[tex]\sqrt[6]{3}[/tex]
h=6
area=[tex]\frac{1}{2} *6*6\sqrt{3}[/tex]
=18[tex]\sqrt{3}[/tex]
Answer: the length of the sides is 6.93 cm
Step-by-step explanation:
In an equilateral triangle, all the sides and angles are equal. The bisectors of each angle meet at the midpoint of the triangle. This means that 3 right angle triangles can be formed. Each of the right angle triangles having angle 60°, 30° and 90°. The altitude of the triangle is the opposite side while the length of each side, x of the equilateral triangle represents the hypotenuse of the right angle triangle.
To find x, we would apply the Sine trigonometric ratio
Sin θ = opposite side / hypotenuse
Sin 60 = 6/h
h = 6/Sin 60 = 6/0.8660
h = 6.93cm
