the sum of the bases and altitude of an isosceles trapezoid is 36 cm.find the altitude if the area is to be maximum.

Question

please help...the sum of the bases and altitude of an isosceles trapezoid is 36 cm.find the altitude if the area is to be maximum.

Answer 1

Hi Emil.

 

The area of a trapezoid is the average of the bases times the altitude

 

A = (1/2) (b₁+b₂)h

 

We know that 

b₁+b₂+h = 36

so,

b₁+b₂=36-h

 

Now Substitute

A = (1/2)(36-h)h

A = 18h-h²/2

 

Take the derivative and set it equal to 0

dA/dh = 18-h = 0

h = 18

 

If h = 18, then b₁+b₂ = 18 and A = (1/2)(18)² = 162 = maximum area