How to find the area of the shaded region in a triangle if: You know that the triangle is composed of two smaller triangles. And, the first small triangle has the base of 5 and you don't know the height. You just know that the other side of the triangle measures 8. And the second smaller triangle has a base of 4....?
Use the Pythagorean theorem on the right triangle on the left to find h:
c² = a² + b²
8² = 5² + h²
64 = 25 + h²
39 = h²
√39 = h
Now that we have the height, we can find the area.
The whole base of the whole big triangle is 5+4 or 9
A = ·b·h
A = ·9·√39
A = 28.10249099 [Round to the number of decimal places your
teacher asks you to]
Edwin