Regular Polygons

Part of the Polygons & Quadrilaterals section of Coddy's Geometry journey. Lesson 6 of 59.

$Three regular hexagons meeting at one point, each corner 120 degrees$

Three regular hexagons meet at this point. Each corner is 120°, and $3\cdot 120^{\circ} = 360^{\circ}$ . So they fill the space around the point with no gap. That is how a honeycomb fits together.

A regular polygon has all sides equal and all angles equal. Matching tick marks show equal sides. Matching arcs show equal angles.

To get one angle, share the angle sum between the corners. A hexagon has 720° and 6 corners, so each angle is $\frac{720}{6} = 120^{\circ}$ . Not every regular shape fills the space around a point like this.

Challenge

A pentagon has 5 sides. Three regular pentagons meet at the point V, like tiles on a floor. Find the gap marked ?. Could regular pentagons cover a floor with no gaps?

Then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

All lessons in Polygons & Quadrilaterals

2Regular Polygons

Regular PolygonsInside a Regular Polygon Recap: Regular Polygons

5Rectangles, Rhombi, Squares

Rectangles The Diagonal of a Rectangle Rhombus Angles Squares Recap: Special Parallelograms

8Area of Parallelograms

Area of a Rectangle A Side from the Area Slide the Top Area of a Parallelogram Recap: Parallelogram Area

11Polygon Chases

Parallel Sides in a Pentagon Marks, Not Looks Pentagon with x Regular Shapes Together Recap: Polygon Chases