+4622 Two points are drawn on each side of a square with an area of 81 square units dividing the side into 3 congruent parts. Quarter-circle arcs connect the points on adjacent sides to create the figure shown. What is the length of the boundary of the bolded figure? Express your answer as a decimal to the nearest tenth.
+9481 The area of the square is 81 square units.
81 un2 = (side length)2
9 un = side length
The two points divide the side length into 3 congruent parts.
So, each piece will be 9/3 = 3 units long. Now we know...
radius of each quarter circle = 3 un and...
length of straight piece = 3 un
On the shape's perimeter...there are 4 quarter circles, and there are 4 straight pieces. So...
perimeter = 4[ circumference of quarter circle ] + 4[ length of straight piece ]
= 4[ (2π * radius)/4 ] + 4[ length of straight piece ]
= [ 2π * radius ] + 4[ length of straight piece ]
= [ 2π * 3 ] + 4[ 3 ]
= 6π + 12
≈ 30.8 un
+9481 The area of the square is 81 square units.
81 un2 = (side length)2
9 un = side length
The two points divide the side length into 3 congruent parts.
So, each piece will be 9/3 = 3 units long. Now we know...
radius of each quarter circle = 3 un and...
length of straight piece = 3 un
On the shape's perimeter...there are 4 quarter circles, and there are 4 straight pieces. So...
perimeter = 4[ circumference of quarter circle ] + 4[ length of straight piece ]
= 4[ (2π * radius)/4 ] + 4[ length of straight piece ]
= [ 2π * radius ] + 4[ length of straight piece ]
= [ 2π * 3 ] + 4[ 3 ]
= 6π + 12
≈ 30.8 un
