Answer:
f(h) = (5h² + 3h) / 2
f(6) = 99 cm²
Step-by-step explanation:
Let's call this function f(h), as we are referring to the base of a triangle in terms of its height.
The equation for the area of a triangle is given by
A = (base * height) / 2
Let's denote height as h and base as b
base b = 5h + 3
Let's substitute base b in terms of h for our area equation
A = ((5h + 3) * h) /2
Expanding this
A = (5h² + 3h) / 2
Written as a function of height then we have
f(h) = (5h² + 3h) / 2
Let's solve for the area of a triangle then who's height is 6 cm
f(6) = (5(6)² + 3(6)) / 2
f(6) = (180 + 18) / 2
f(6) = 198 / 2
f(6) = 99 cm²
