Angles are 30-60-90 degrees.
Hypotenuse = 12
One leg = 6
Other leg = 6 sqrt(3)
Area = 1/2 (base) x (height) = (1/2) (6) [ 6 sqrt(3) ] = 18 sqrt(3) = 31.177 square units.
Sin 30 = perpendicular/ Hypotenuse
=Perpendicular/ 12
Perpendicular = 12x1/2 = 6
By Rt. angle triangle formula i.e. (Hyp)2 = (Base)2 + (Per)2
Base = sqrt (3)
Area = 1/2 (base) x (height) = (1/2) (6) [ 6 sqrt(3) ] = 18 sqrt(3) = 31.177 square units
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The hypotenuse only is not sufficient to determine the area of a right triangle, unless the triangle is stated to be isosceles, or there is some other information that allows determination of the length of a side in addition to the hypotenuse. The area of a right triangle with a given hypotenuse only approaches zero as one of the two acute angles approaches zero degrees.
The hypotenuse of a right triangle with legs 12 inches and 16 inches is: 20 inches.
hypotenuse = sqr ( 5² + 12² ) = 13.
Area = 1/2*9*12 = 54 square cm
If the hypotenuse is the square root of three, then the legs are (root 6)/2. If the hypotenuse is 12, then the legs are 6(root 2). This is because, for any given right isosceles triangle, the length of the hypotenuse x is root two times the length of the legs.