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Sunny_sXe [5.5K]
3 years ago
13

Area addition and subtraction

Mathematics
1 answer:
sertanlavr [38]3 years ago
6 0

Answer:

3.8 in^{2}

Step-by-step explanation:

We are given a square of size 6x6 in. So, area of this square is equal to 6 x 6 = 36 in^{2}. Now, the shaded region is \frac{1}{2} x (Area of square - area of semicircles)

The diameter of both semicircles = side of the square = 6in

So, radius (r) = \frac{1}{2} x diameter = \frac{1}{2} x 6 = 3in

And hence, area of semicircle is  = \frac{1}{2} x πr^{2}

= \frac{1}{2} x π3^{2}

Since, there are two semicircles we multiply above by 2, so area of both semicircles = 2 x \frac{1}{2} π3^{2} = 9π

Area of shaded region =  \frac{1}{2} (36 - 9π) = 3.8628 = 3.8 in^{2} to the nearest tenth.

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