The plane is tiled by congruent squares of side length $a$ and congruent pentagons of side lengths $a$ and $\frac{a\sqrt{2}}{2}$
1 answer:
The percentage of this plane that's enclosed by the pentagons is closest to: D. 56.
<h3>How to determine the percentage?</h3>Since the side of the small square is a, then the area of the tile is
given by:
Area of tiles = 9a²
<u>Note:</u> With an area of 9a², 4a² is covered by squares while 5a² by pentagons.
This ultimately implies that, 5/9 of the tiles are covered by pentagons and this can be expressed as a percentage as follows:
Percent = 5/9 × 100
Percent = 0.555 × 100
Percent = 55.5 ≈ 56%.
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Complete Question:
The plane is tiled by congruent squares of side length a and congruent pentagons of side lengths a and a²/a, as arranged in the diagram below. The percent of the plane that is enclosed by the pentagons is closest to (A) 50 (B) 52 (C) 54 (D) 56 (E) 58
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