Quadrillateral

A circle is inscribed in a rectangle such that it contacts each side of the rectangle at exactly one point. The area of the circle is 16Ï€. What is the area of the rectangle?

If a circle contacts each side of the rectangle at exactly one point, then the rectangle is certainly a square. Since the circle is inscribed in a square and since it touches all the sides, the length of the side of the square is equal to the diameter of the circle.

Area of circle of radius r = π*r*r = 16π. r*r = 16 and r = 4.
Diameter of the circle = 2r = 8
Area of the sqaure = side * side = diameter * diameter = 8*8 = 64 square units.

A rectangle has a width of 5 and a length of 6. If the width of the rectangle is reduced by 2, and the length is increased by 7, then the resulting area is what percent greater than the area of the original rectangle?

Length of the rectangle = 6 units
Width of the rectangle = 5 units.
Area of the rectangle = Length of the rectangle * Length of the rectangle = 6*5 = 30 square units.

Length of the new rectangle = 6+7 = 13 units
Width of the new rectangle = 5-2 = 3 units.
Area of the new rectangle = Length of the new rectangle * Width of the new rectangle = 13*3 = 39 square units.

Resulting area = ((39-30)/30)*100 = 30% Greater than the area of the original triangle.

Number 3:

Let the radius of the circles be r.
Area of the circle = pi*r*r = 16*pi. r*r = 16. r = 4

Then the length of the rectangle = 8r
and the width of the rectangle = 2r
Area of the rectangle = Length of the rectangle * Width of the rectangle = 8r*2r = 16*r*r = 16*4*4 = 256