Open Middle®
Directions: Using the digits 1 to 6, at most one time each, place a digit in each box to create the largest possible combined area for the rectangle and circle.
Hint
Which numbers would yield a greater area?
Which numbers would yield the greatest area for just the rectangle?
Which number would yield the greatest area for the just the circle?
How can you combine these to find the greatest combined area?
Which numbers would yield the greatest area for just the rectangle?
Which number would yield the greatest area for the just the circle?
How can you combine these to find the greatest combined area?
Answer
The largest area is found by having a circle with radius of 4 and the dimensions of the rectangle are 6 by 53. Total area is about 368.24 square units.
Source: Mike Chamberlain
I was experimenting and found the lowest number possible. With a radius of 3, and base of 24, and a height of 1, I ended up with a 52.27433388.
One of my students came up something lower. A radius of 2, base of 34, and height of 1 makes an area of 46.56.
Should this be titled “Rectangle and Circle Area” instead? Some of my students were mislead and thought the rectangle had to be a square.
I just created a document to share with my students & made that exact change.
Ditto Zach’s comment – you should change the name.