Question

Find the area of the shaded region

Answer 1

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 $= (l)(w) = (12)(6) = 72$ square cm.

The area of each circle $= \pi r^{2} = (3.1415)(3^{2} ) = 28.2735$ square cm.

The area of both circles $=2(28.2735) = 56.547$ 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 $= 72 - 56.547 = 15.453$ square units.

The area of the shaded region is 15.453 square units.