Question

find the area of the yellow shaded region. 8 cm area = ? cm² round to the nearest tenth

Explanation:

Step1: Calculate area of square

The side - length of the square is $s = 8$ cm. The area of a square is $A_{square}=s^{2}$. So, $A_{square}=8^{2}=64$ cm².

Step2: Calculate area of four quarter - circles

The four quarter - circles together form a complete circle. The radius of each quarter - circle is $r=\frac{8}{2}=4$ cm. The area of a circle is $A_{circle}=\pi r^{2}$, where $\pi\approx3.14$ and $r = 4$ cm. So, $A_{circle}=3.14\times4^{2}=3.14\times16 = 50.24$ cm².

Step3: Calculate area of shaded region

The area of the shaded region $A$ is the area of the square minus the area of the circle. So, $A=A_{square}-A_{circle}=64 - 50.24=13.76\approx13.8$ cm².

Answer:

$13.8$ cm²