The above diagram shows two right triangles 6-8-10 and 8-15-17 joined to form a large triangle with side lengths 10-17-21.
What is the area of this large triangle?
By the Pythagorean Theorem the height of the large triangle is given by
sqrt [ 10^2 - 6^2 ] = sqrt [100 - 36 ] = sqrt (64) =8
So the area of the large triangle is given by
(1/2) (base) (height) =
(1/2) ( 6+15) (8) =
(1/2) (21) (8) =
4 * 21 =
84 units^2
You can solve this one in your head in less then a minute.
A = 4*6 + 4*15
