Answer:
Option 2 - 402 m sq.
Step-by-step explanation:
Given : Laura's yard is in the shape of a square and a half-circle.
To find : What is the approximate area of Laura's yard?
Solution :
The side of the square is 17 m
The area of the square is [tex]A_s=s^2[/tex]
[tex]A_s=17^2[/tex]
[tex]A_s=289m^2[/tex]
The half circle form upon a square side.
So, The diameter of the half circle is equal to the side of the square.
d=17 m
Radius of the half circle is [tex]r=\frac{17}{2}[/tex]
The area of the half circle is [tex]A=\frac{1}{2} \pi r^2[/tex]
Substitute the value in the formula,
[tex]A_c=\frac{1}{2}\times \frac{22}{7}\times(\frac{17}{2})^2[/tex]
[tex]A_c=\frac{22\times 17\times 17}{2\times 7\times 2\times 2}[/tex]
[tex]A_c=\frac{6358}{56}[/tex]
[tex]A_c=113.53m^2[/tex]
Total area of the Laura's yard is
[tex]A=A_s+A_c[/tex]
[tex]A=289+113.53[/tex]
[tex]A=402.53m^2[/tex]
Approximately the area of the Laura's yard is 402 m sq.
Therefore, Option 2 is correct.
