I'm not sure what you are asking, so I may not be answering your question, but I'll try to the best of my ability.
This is only for RIGHT TRIANGLES
*Another way to find the other side beside the shortcut is by using the Pythagorean Theorum (a2+b2=c2) if you are given the other two side measurements.*
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To find the altitude or height of an equilateral triangle, take one-half of the length of a side of the triangle and multiple by "square root" of 3. So, if for example, the side has length 10, the height = 5 Square root of 3.
2.08cm. To find the area of any triangle - divide the length of the base by 2, then multiply the result by the height.
Base = 8, Height = 15
By using Pythagoras' theorem.
Use Pythagoras to find the perpendicular height of the triangle: 132-52 = 144 and the square root of this is the height of the triangle which is 12 cm Area = 1/2*12*10 = 60 square cm