If it is a right triangle, you can use the Pythagorean theorem to find the height since it will be
on of the sides.
If it is an equilateral triangle, you can break it up into two right triangles and use the part above.
If it is an oblique triangle, you use the angles and some trigonometry to find it.
Since the area is 1/2 b x h, if you are given the area, you can solve for the height.
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Finding the perpendicular height of the triangle by using Pythagoras works out at about 8.660254038. 1/2*base*perpendicular height or altitude = area 1/2*10*8.660254038 = 43.30127019 square units
Area of any triangle: 0.5*base*perpendicular height
Base times Height divided by three. The base is perpendicular to the height, which ends at the highest point of the pyramid. To find the area of the base, one simply uses 2-dimensional geometry. Triangle: Base of triangle times height of triangle over 2 Any regular polygon: Apothem (perpendicular distance from orthocenter to a side) times perimeter divided by 2.
Area = 1/2*base*perpendicular height.
Area of a scalene triangle: 0.5*base*perpendicular height