Answer:
Area of extra Between Circles; 384 - 80π,
Perimeter of Rectangle; 80
Explanation:
We have to solve for ⇒ extra area between circles circumscribed in the rectangle, perimeter of the Rectangle;
Now let us first identify the area of each circle, perhaps in terms of π for the moment being;
Area of Larger Circle ⇒ πr^2, π * ( 8 )^2, π * 64, ⇒ 64π
Area of Smaller Circle ⇒ πr^2, π * ( 4 )^2, π * 16, ⇒ 16π
Now knowing that radius of larger circle ⇒ 8 units, and the radius of the smaller circle ⇒ 4 units, we can see the length of this rectangle that " circumscribed " these circles to be;
Diameter of Larger Circle + Diameter of Smaller Circle ⇒ 8 * 2 + 4 * 2 ⇒ 16 + 8 ⇒ Dimension of Rectangle: 24 units long,
This other dimension of the rectangle can also be computed through such;
Diameter of Larger Circle ⇒ Other Dimension of Rectangle : 16 units long,
From the two dimensions we can derive the area of this rectangle ( through multiplication of length * width ) and the perimeter of the same rectangle ( 2 * length + 2 * width );
Area of Rectangle ⇒ length * width = 24 * 16 = 384 units^2
Perimeter of Rectangle ⇒ 2 * length + 2 * width = 2 * 24 + 2 * 16 = 48 + 32 = 80 units^2
Perimeter of Rectangle; 80
Knowing the area of the rectangle and the area of the two circles, we can compute the area between these circle as well, as such;
Area of extra between Circles ⇒ Area of Rectangle - Area of Circle 1 - Area of Circle 2 = 384 - 64π - 16π, 384 - 80π
Area of extra Between Circles; 384 - 80π