Two identical rectangles, ABCD and EF GH, each with area 13 cm2, overlap as
shown. The area of the overlapped region, rectangle EF CD, is 5 cm2. What is
the area of rectangle ABGH?

 

 

Largest Area A rectangle is to be inscribed in a semicircle of radius 5 cm as shown in the following figure.

(a) Show that the area of the rectangle is modeled by the function 

(b) Find the largest possible area for such an inscribed rectangle. [ Hint: Use the fact that sin u achieves its maximum value at ].

(c) Find the dimensions of the inscribed rectangle with the largest possible area.  

Find the maximum area of a rectangle that can be circumscribed about a given rectangle with length L and width W. [Hint: Express the area as a function of an angle .]

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The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s. When the length is 20 cm and the width is 10 cm . How fast is the area of rectangle increasing?