Find the area of the largest trapezoid that can be inscribed in a circle of radius 1 and whose base is a diameter of the circle.

Question

Mathematics

Cedric Wilkerson

23 August, 08:31

Find the area of the largest trapezoid that can be inscribed in a circle of radius 1 and whose base is a diameter of the circle.

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Answers (1)

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Noah Harvey · Answer 1

let x = shortest base of the trapezoid

A = h (x/2 + r) = âš (rÂ˛ - (x/2) Â˛) (r + x/2)

= âš (1 - (x/2) Â˛) (1 + x/2) ... if r = 1

dA/dx = (2 - x - xÂ˛) / (2âš (4 - xÂ˛))

= 0 at x = 1 ... which is a relative maximum because dÂ˛A/dxÂ˛ < 0

A = (3/4) âš3