Aright triangle has a hypotenuse of length 17 and a leg of length 13 what is the area

71.2 units2(squared)

If the base of the triangle is the leg that is 13 then the leg that is not known (because it is a right angle triangle) is the perpendicular height. 
As the Area of a triangle = 1/2 * base * height, we first must calculate the height. 

Using Pythagoras's Theorem that states that "The square of the hypotenuse is equal to the sum of the squares of the other two sides" 
17^2 = 13^2 + height^2 
289 = 169 + height^2 
Subtract 169 from both sides of the equation 
120 = height^2 
Therefore height = sqrt(120) 

Therefore Area of triangle = 1/2 * 13 * sqrt(120) 
= 6.5 * 10.95445115 
= 71.20393248 
= 71.20 to two decimal places


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