Answer:
[tex]648\ yd[/tex]
Step-by-step explanation:
step 1
Find the circumference of the complete circle
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=35\ yd[/tex]
substitute
[tex]C=2\pi(35)[/tex]
[tex]C=70\pi\ yd[/tex]
step 2
Find the measure of the arc length for a central angle of 280 degrees
Remember that the circumference subtends a central angle of 360 degrees
so by proportion
[tex]\frac{70\pi}{360}=\frac{x}{280}\\ \\x=280*(70\pi )/360\\ \\x=54.44\pi\ yd[/tex]
step 3
Find the perimeter of the playground
[tex]P=54.44\pi+45=54.44*3.14+45=215.96\ yd[/tex]
Multiply by 3
[tex]215.96*(3)=647.87\ yd[/tex]
Round to the nearest integer
[tex]647.87=648\ yd[/tex]
