area of a rectangle with six unit circles inside

Question

six unit circles are arranged inside a rectangle. the circles are tangent to each other and tangent to the rectangle. what is the area of the rectangle?

Answer 1

Hello Julie!

 

The answer to your question is this: 

No matter if the six circles are all side-by-side, or in two rows of three circles each, the area of the rectangle will be the same:

 

The diameters of each circle will be added to determine the base and height of the rectangle.

In the first case, the rectangle's height will be 1 unit, and its base will be 6 units for an area of 6 square units.

In the second example, the rectangle's height will be 2 units, and its base will be 3 units for an area of 6 square units.

 

Hope this helps!

Answer 2

a unit circle is a circle whose radius is 1 unit

if the radius is 1 unit the diameter is 2 units

if the 6 circles are in a straight horizontal line, the length of the rectangle is 6 diameters long

6 diameters is 6*2=12 units

the width is 1 diameter long , or 2 units

A=lw

A=12*2=24 square units

if the circles are 3 in a row and then 3 in a row underneath, the length of the rectangle is 3 diameters or 3*2=6 units

the width is 2 diameters or 2*2=4 units

A=lw

A=6*4=24 square units