Question

Find the area of an equilateral triangle whose base is 10 cm.

Answer 1

2 right angled triangles = 1 equilateral triangle. You can pretty much split it down the middle and you'll see the 2 triangles from.

The formula for a right angle triangle is:
(b x h)/2 = area

If we were solving for 1/2 the triangle we know that the base is 5 cm, the height is unknown and the hypotenuse is 10 cm.

Using Pythagorean theorem we can solve for the height:
a^2 + b^2 = c^2
5^2 + b^2 = 10^2
25 + b^2 = 100
b^2 = 75
b = about 8.66

Now we can plug this value for our height back into the equation:
(b x h)/2 = area
(5 x 8.66)/2 = area
21.65 cm^2

Remember this is only 1/2 of the triangle so you could multiple by 2 (or simply do not divide my 2 in the above equation):
Area of equilateral triangle = 43.30 cm^2

Answer 2

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