Pythagorean Theorem

In any right triangle the sum of the square of the two legs is always equal to the square of the hypotenuse ( the side across the right angle). In other words:
 
a2 + b2 = c2

 
 
 

Example 1) Find the area:

The formula for the area of a triangle is A= ½ bh. We know the base of this triangle has length 10. The height is the line segment from the top of the triangle perpendicular to the base. Since the height makes a right angle with the base we can use the Pythagorean Theorem in the triangle formed by the height. Since the original triangle is isosceles (has two equal sides), the height will divide the base in half.
 

52 + h2 = 132
25 + h2 = 169
h2 = 169 – 25
h2 = 144
h = = 12
So the area is A= ½ (10)(12)
A = 60.

 

Practice Problems:

Find the area:

4. 
 
 
 
 

5. 
 

Solutions:


4. 

32+x2=52 Þ 9+x2=25 Þ x2=16 Þ x=4.
A= (4)(3)= 12


 
 

5. 
 
 

x2+52=132 Þ x2 +25 =169 Þ x2=144 Þ x=12.
A = = 6.25pi + 30

Copyright © 1997 Bamdad Samii