SOLUTION: A Rectangle is inscribed in a semicircle of radius 10. Find a function that models the area (A) of the rectangle in terms of its Height (H). WOW! I don't even know how to begin

Question 274701: A Rectangle is inscribed in a semicircle of radius 10. Find a function that models the area (A) of the rectangle in terms of its Height (H).
WOW! I don't even know how to begin on this one. The answer is the textbook is A(h)=2h times square root of 100-h squared.
Please help!
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the rectangle sits centered on the diameter with the upper corners touching the semicircle

two radii drawn to the upper corners divide the rectangle into three triangles

the area of one of the smaller outer triangles is equal to 1/4 of the area of the rectangle
(bisecting the larger central triangle shows the 4 smaller congruent triangles)

the hypotenuse of the triangle is the radius (10)
the height of the triangle is the height of the rectangle (h)

by Pythagoras, the base of the triangle is ___ sqrt(100 - h^2)

the area of the triangle is ___ (1/2) (h) (sqrt(100 - h^2))

the area of the rectangle is 4 times the triangle
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