Wednesday

July 30, 2014

July 30, 2014

Posted by **soffy** on Monday, June 11, 2012 at 10:49am.

- calculus -
**Steve**, Monday, June 11, 2012 at 11:06amFor lack of specificity, I will let θ be the angle between the upper base and a side. I expect it will end up 90°, making a square cross-section, but let's wee what happens.

The height of the trapezoid will be 10sinθ, so the area is

a = 10sinθ (10+10+2*10cosθ)

= 10sinθ (20+20cosθ)

= 200sinθ (1+cosθ)

da/dθ = 200cosθ (1+cosθ) + 200sinθ(-sinθ)

= 200(cos^2θ + cosθ - sin^2θ)

= 200(2cos^2θ+cosθ-1)

da/dθ = 0 when cosθ = 1/2 or -1.

Looks like the max area occurs at θ=π/3

Looks like my gut feeling was wrong. Good thing, as it would have been a boring trapezoid.

- calculus - correction -
**Steve**, Monday, June 11, 2012 at 11:07amOops. I forgot to divide by 2 when getting the average of the bases, but that does not affect the answer in this case.

**Related Questions**

calculus - a trapezoid is a quadrilateral with (only) two sides (called bases) ...

maths - A large canal will have a cross-section in the shape of an isosceles ...

math - The cross section of an attic is in the shape of an isosceles trapezoid. ...

Geometry - An engineer designed a 620 ft long water canal to drain a rainwater ...

calculus - A water-trough is 10m long and has a cross-section which is the shape...

fd - a trapezoid abcd has parallel sides ab and dc of lengths 8 and 22. If both ...

geometry - the longer base of an isosceles trapezoid is 14 feet. the nonparallel...

Please help with a trapezoid - circle problem - A circle with radius 3 is ...

geometry - I have a isosceles trapezoid question. The top line is 13" long, the ...

geometry - a trapezoid has an area of 5 1/2 feet squared. if the trapezoid has a...