+0  
 
0
438
1
avatar+3171 

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.

 

tertre  Jul 23, 2017

Best Answer 

 #1
avatar+7324 
+1

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

hectictar  Jul 23, 2017
 #1
avatar+7324 
+1
Best Answer

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

hectictar  Jul 23, 2017

24 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.