The area of the shaded region is 15.453 square units.
Step-by-step explanation:
Step 1:
The given shape consists of a rectangle and two circles.
The length of the rectangle is given as 12 cm. Both the diameters of the circles equal 12 cm. So each circle has a diameter of 6 cm and thus a radius of 3 cm.
The diameter of the circle is equal to the width of the rectangle.
So the rectangle has a length of 12 cm and a width of 6 cm. The circles have radii of 3 cm each.
Step 2:
The area of the rectangle [tex]= (l)(w) = (12)(6) = 72[/tex] square cm.
The area of each circle [tex]= \pi r^{2} = (3.1415)(3^{2} ) = 28.2735[/tex] square cm.
The area of both circles [tex]=2(28.2735) = 56.547[/tex] square cm.
The area of the shaded region is the difference between the area of the rectangle and the area of both circles.
The area of the shaded region [tex]= 72 - 56.547 = 15.453[/tex] square units.
The area of the shaded region is 15.453 square units.
