[Calculus] A gutter is to be made of a strip of metal 22.8 inches wide, with the cross-section having the form of an isosceles trapezoid

Question

A gutter is to be made of a strip of metal 22.8 inches wide, with the cross-section having the form of an isosceles trapezoid as shown below. Find the depth h that gives the maximum cross-sectional area.

What is the length of a in the picture? __

The depth, h, that gives the maximum cross-sectional area is ___

The maximum cross-sectional area is__

Answer 1

Filling in data

3a = 22.8

a = 7.6

Using Pythagoras determine h in terms of a

The area of the cross-section is the sum of 2 triangles and a rectangle.

Express the area in terms of h and take first derivative.