How do you find the largest area of a rectangle inscribed in a semicircle?

How do you find the largest area of a rectangle inscribed in a semicircle?

Let r be the radius of the semicircle, x one half of the base of the rectangle, and y the height of the rectangle. We want to maximize the area, A = 2xy. Thus, the base of the rectangle has length = r/√2 and its height has length √2*r/2.

What is the largest area of a rectangle that could be inscribed in a semi circle having a radius of 10m?

A rectangle is inscribed in a semicircle of radius 10 cm. What is the area of the largest rectangle we can inscribe? Amax = xw = (5 / 2)(10 / 2) = 100 Page 7 A poster is supposed to have margins of 1 inch on the left and right and 1.5 inches on top and on bottom. The printed area is supposed to be 54 square inches.

What is the area of the largest rectangle that can be inscribed in a semicircle of radius 5cm?

25 square units
The area of the largest rectangle that can be inscribed in a semi-circle of radius 5 is 25 square units.

What is the area of the largest rectangle that can be inscribed in a semi circle of radius 2m?

The answer is 8 sq. units. It can be easily proven that the largest rectangle in a given circle is a square.

What is the area of the largest rectangle that can be inscribed in an ellipse?

Thus the maximum area of a rectangle that can be inscribed in an ellipse is 2ab sq. units.

What is the area of semicircle?

Area of Semi Circle The area of a semicircle is half of the area of the circle. As the area of a circle is πr2. So, the area of a semicircle is 1/2(πr2 ), where r is the radius.

Which of these rectangle has biggest area?

4 Answers. The result you need is that for a rectangle with a given perimeter the square has the largest area. So with a perimeter of 28 feet, you can form a square with sides of 7 feet and area of 49 square feet.

What is the largest rectangle that can be inscribed in a circle?

The largest rectangle that can be inscribed in a circle is a square. The usual approach to solving this type of problem is calculus’ optimization. An algebraic solution is presented below. Consider Fig. 1. A rectangle is inscribed in a circle whose equation is x where r is the radius of the circle.

How to find the area of a rectangle with a semicircle?

Let r be the radius of the semicircle, x one half of the base of the rectangle, and y the height of the rectangle. We want to maximize the area, A = 2xy. Thus, the base of the rectangle has length = r/√2 and its height has length √2*r/2 . Attention reader!

How to find the maximum value of the area of a rectangle?

To find the maximum value of the area, we find where the derivative is equal to zero. This is the area of the rectangle inscribed in the circle x 2 + y 2 = 1. To find the maximum value of the area, we find where the derivative is equal to zero. A = 2 (1/ (root 2))*2 (1/ (root 2)) = 2 square units.

How do you find the area of a circle with maximum area?

To have maximum area , the rectangle inside the circle must be symmetrically situated. Now the area of such a rectangle inside the circle A = (2x) (2y) = 2sin2θ . Clearly A is maximum if sin2θ is maximum. But max. Value of sin2θ is 1 and it is attained here when 2θ = (pi/2) or θ = (pi/4) and the max. Value of A = 2 sin (pi/2) = 2 .