Garage Door

Geometry Level 4

This is a 96" x 96" section of a garage door. This image is a square of equal sides.

There are four rows in this square section. Each row shows 3 full rectangles and 2 parts of rectangles. Each rectangle is approximately 14" x 19". The rectangles are separated by some vertical pieces approximately 14" long. The rows are spaced 8.5" apart, and the top and bottom rows are spaced from the top and bottom of the image by 7.25", i.e. 4(14)+3(8.5)+2(7.25)=96.

Approximately what percent of the area of this image is covered with circles, which are visible in this image?

Give answer to nearest percent %

You may use a ruler to directly measure the diameter of the circles, which are not tiny.

13 6 27 41 20 34

1 solution

Michael Mendrin
Aug 7, 2017

Here is one of the circles, marked in red, which has a diameter of approximately 14". There are 16 such identical circles in a regular 4 x 4 array. The percent coverage then works out as follows

$100\left( \dfrac { 16\pi { 7 }^{ 2 } }{ { 96 }^{ 2 } } \right) =26.7254...\approx 27$ %

The circles are defined by all the vertical lines in this image. Elimination of the horizontal lines will clearly bring out the circles.

Garage Door

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