Introduction to Polygons

Show your work for each problem.

1.
Which of these shapes is a polygon?
1. a)Triangle
2. b)Circle
3. c)Curved line
4. d)Spiral
Answer: Triangle
A triangle is the only polygon here. It has straight sides and is closed. Circles and curves are not polygons because they don't have straight sides.
2.
How many sides does a hexagon have?
Answer: 6
A hexagon has 6 sides. The prefix 'hexa-' comes from Greek and means six.
3.
What shape is a stop sign?
1. a)Octagon
2. b)Hexagon
3. c)Pentagon
4. d)Rectangle
Answer: Octagon
A stop sign is an octagon, which has 8 sides. This unique shape helps drivers recognize it quickly, even from a distance.
4.
How many vertices does a triangle have?
Answer: 3
A triangle has 3 vertices (corners). In any polygon, the number of vertices equals the number of sides.
5.
Why is a circle NOT a polygon?
1. a)It's too small
2. b)It has too many sides
3. c)It's not flat
4. d)It has no straight sides
Answer: It has no straight sides
A circle is not a polygon because it has no straight sides. Polygons must be made of straight line segments. A circle is one continuous curve.
6.
A shape has 5 sides. What is it called and how many vertices does it have?
Answer: pentagon, 5
1. What prefix means 5? penta
2. What is a 5-sided polygon called? pentagon
3. How many vertices does it have? (Vertices = Sides) 5
7.
Which polygon has 4 sides and 4 vertices?
1. a)Quadrilateral
2. b)Triangle
3. c)Pentagon
4. d)Hexagon
Answer: Quadrilateral
A quadrilateral has 4 sides and 4 vertices. Examples include squares, rectangles, trapezoids, and rhombuses.
8.
If a polygon has 8 vertices, how many sides does it have?
Answer: 8
A polygon with 8 vertices has 8 sides. This polygon is called an octagon. The number of vertices always equals the number of sides.
9.
Is the letter 'L' a polygon? Explain why or why not.
Answer: no, not closed
1. Does the letter 'L' have straight sides? yes
2. Is the letter 'L' a closed shape (no openings)? no
3. So is 'L' a polygon? no
10.
What makes a polygon 'regular'?
1. a)It has no curves
2. b)It has an even number of sides
3. c)All sides equal AND all angles equal
4. d)It has more than 6 sides
Answer: All sides equal AND all angles equal
A regular polygon has all sides equal in length AND all angles equal in measure. Examples: equilateral triangle, square, regular hexagon.
11.
What is the name of a polygon with 7 sides?
Answer: heptagon
A 7-sided polygon is called a heptagon. 'Hepta-' is a Greek prefix meaning seven.
12.
A honeycomb cell is a regular hexagon. If a honeycomb has 10 cells in a row, how many sides would you count if you traced around the outer edge?
Answer: 42
1. How many sides does each hexagon have? 6
2. When hexagons share sides, how many sides are exposed on top and bottom of each cell? 2
3. For 10 cells, that's 10 × 2 = ? 20
4. Plus 2 end sides (left and right), total = ? 22
13.
Which of these is NOT a quadrilateral?
1. a)Trapezoid
2. b)Rectangle
3. c)Rhombus
4. d)Pentagon
Answer: Pentagon
A pentagon has 5 sides, so it is NOT a quadrilateral. Rectangles, trapezoids, and rhombuses all have 4 sides, making them quadrilaterals.
14.
A soccer ball is made of pentagons and hexagons. If a standard soccer ball has 12 pentagons and 20 hexagons, how many total polygon faces does it have?
Answer: 32
1. How many pentagons are there? 12
2. How many hexagons are there? 20
3. Total faces = pentagons + hexagons = ? 32
15.
What is the name of a 10-sided polygon?
Answer: decagon
A 10-sided polygon is called a decagon. The prefix 'deca-' means ten, as in decade (10 years) or decathlon (10 events).
16.
Is a 3D shape like a cube a polygon? Explain your reasoning.
Answer: no, not flat
1. Is a cube flat (2D)? no
2. What dimension must a polygon be? 2D
3. So is a cube a polygon? no
4. But what shape are the faces of a cube? square