Finding the area of a rectangle?

Question

Not sure how to do this...any help would be appreciated.

1.) A rectangle is inscribed in a semicircle of radius 2. What is the largest area of the rectangle?

Answer 1

Shetch the semi circle with rectangle contained therein.
Draw radius r = 2 such that r makes angle θ
with horizontal at centre of circle.
Horizontal component of r = 2 cos θ so base of rectangle = 4 cos θ
Vertical component of r = r sin θ = 2 sin θ
Area of rectangle = 4 (cos θ) (2 sin θ)
A = 8 sin θ cos θ
A = 4 (2 sin θ cos θ)
A= 4 sin 2θ
A max = 4 units ²

Answer 2

You should note that the area of the rectangle is 2xy where (x,y) is a point on the circle, making it easy to write y in terms of x. Then do your max/min procedures. The value for "x" is close to 1.2 and "y" is close 1.6, but these are the correct values.

Answer 3

the area is the square root of 15

Answer 4

You just measer the long side on the bottom and the short side going up and you times those two numbers
P.S. that is so easy!!!!!