Find the area of the shaded region. Express your answer in terms of pi

The area of shaded region is,  

From given figure, it is observed that unshaded region is sum of  area of three circles.

Diameter of first circle = 12 inch ,  radius = 12/2 = 6 inch

Diameter of second circle = 9 inch ,  radius = 9/2 = 4.5 inch

Diameter of third circle = 6 inch , radius = 6/2 = 3 inch

Area of circle = , where r is radius of circle.

Dimension of rectangle is,

 length = 12 + 9 + 6 +3 = 30 inch

width = 18 inch

Shaded area = Area of rectangle  - sum of area of three circles.

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Area of the shaded region is 540 – 65.25π.    

Solution:

Length of the rectangle = 12 + 9 + 6 + 3 = 30 in

Width of the rectangle = 18 in

Radius of the larger circle () = 12 ÷ 2 = 6 in

Radius of the medium circle () = 9 ÷ 2 = 4.5 in

Radius of the smaller circle () = 6 ÷ 2 = 3 in

Area of the shaded region = Area of the rectangle – Area of the larger circle – Area of the medium circle – Area of the smaller circle

Area of the shaded region is 540 – 65.25π.    

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

m∠5 + m∠3 = m∠1   is true.

m∠5 + m∠6 = 180 is true

m∠2 +m∠3 = m∠6   is true

m∠2 +m∠3 +m∠5 = 180   is true