Answer:
120 cm²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
We require to calculate h
The segment from the vertex to the base is a perpendicular bisector.
This divides the triangle into 2 right triangles, with legs 8 and h and hypotenuse 17.
Using Pythagoras' identity on the left right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
h² + 8² = 17²
h² + 64 = 289 ( subtract 64 from both sides )
h² = 225 ( take the square root of both sides )
h = [tex]\sqrt{225}[/tex] = 15, thus
A = 0.5 × 16 × 15 = 8 × 15 = 120 cm²
