Question

Find the area of the yellow region. Round to the nearest tenth.

Answer 1

You have a square and four quarter circles with a radius of 4.

The area is

${ 8}^{2} - 4 \times \frac{90}{360} \pi \times {4}^{2} \\ = 64 - 4 \times \frac{1}{4} \pi \times 16 \\ = 64 - \pi \times 16$

Put that into your calculator and get the answer.

Answer 2

Answer:

The area of yellow region is:

                    13.8 cm^2

Step-by-step explanation:

The area of the yellow region is the area of square minus 4 times the area of one half semicircle at the corner of the square.

These four half semicircle will form a complete circle.

This means that the area of 4 half semicircles is equal to the area of the circle.

Hence, the area of yellow region is:

Area of square-Area of circle of radius 4 cm.

Also, the radius(r) of circle is: 4 cm.

and the area of circle is given by: $\pi r^2$

i.e.

$Area\ of\ circle=3.14\times 4^2\\\\i.e. \\\\Area\ of\ circle=50.24\ cm^2$

Area of square is: $s^2$

where s is the side length of the square.

Here

$s=8\ cm.$

Hence,

$Area\ of\ square=8^2\\\\Area\ of\ square=64\ cm^2$

Hence, Area of yellow region is:

$=64-50.24\\\\=13.76\ cm^2$

which to the nearest tenth is: 13.8 cm^2