In the figure below, is a triangle, where ,
Find the area of .
Step 1: Find the length of (the height of the
Use Pythagoras' theorem, which states that the square of the
length of a right-angled triangle's hypotenuse is equal to the sum
of the squares of the lengths of the other two sides.
Step 2: Find the length of (the triangle's base).
If the hypotenuse and one other side of a right-angled triangle are congruent to the corresponding parts of another right-angled triangle, then the two triangles are congruent.
Since , and is a common side, then
, and the corresponding sides are equal in length.
Step 3: Find the area of .