Classifying Polygons

Show your work for each problem.

1.
Which shape is a polygon?
1. a)Triangle
2. b)Curved line
3. c)Circle
4. d)Oval
Answer: Triangle
A triangle is the only polygon because it has straight sides. Circles, ovals, and curved lines are not polygons because they have no straight edges.
2.
How many sides does a hexagon have?
Answer: 6
A hexagon has 6 sides. The prefix "hexa-" comes from the Greek word for six. Honeycomb cells are a common example of hexagons.
3.
What is the name of a polygon with 8 sides?
1. a)Decagon
2. b)Hexagon
3. c)Octagon
4. d)Heptagon
Answer: Octagon
An octagon has 8 sides. The prefix "octa-" means eight. STOP signs are the most recognizable octagons in everyday life.
4.
A shape has 5 sides. What is it called?
Answer: pentagon
A 5-sided polygon is called a pentagon. The U.S. Department of Defense building is famous for its pentagonal shape.
5.
Identify the polygon: a closed shape with 3 straight sides.
Answer: triangle
1. Is this shape a polygon? (yes/no) yes
2. How many sides does it have? 3
3. What is a 3-sided polygon called? triangle
6.
Which of these is NOT a quadrilateral?
1. a)Square
2. b)Trapezoid
3. c)Rectangle
4. d)Pentagon
Answer: Pentagon
A pentagon has 5 sides, not 4. Squares, rectangles, and trapezoids all have exactly 4 sides, making them quadrilaterals.
7.
A decagon has how many sides?
Answer: 10
A decagon has 10 sides. The prefix "deca-" means ten, just like "decade" means ten years.
8.
A polygon has 7 angles. How many sides does it have, and what is it called?
Answer: heptagon
1. In a polygon, what equals the number of angles? sides
2. So if there are 7 angles, how many sides? 7
3. What is a 7-sided polygon called? heptagon
9.
Which polygon is used for STOP signs?
1. a)Pentagon
2. b)Heptagon
3. c)Octagon
4. d)Hexagon
Answer: Octagon
STOP signs are octagons (8 sides). This unique shape helps drivers recognize them instantly, even from behind or in poor visibility.
10.
Classify this shape: a closed figure with 4 equal sides and 4 right angles.
Answer: square
1. Is it a polygon? (yes/no) yes
2. How many sides does it have? 4
3. What type of polygon has 4 sides? quadrilateral
4. With all sides equal AND all angles equal, is it regular? (yes/no) yes
5. What is a regular quadrilateral with right angles called? square
11.
A honeycomb cell is what type of polygon?
Answer: hexagon
Honeycomb cells are hexagons (6 sides). Bees use this shape because hexagons tessellate (fit together with no gaps), maximizing storage space with minimal wax.
12.
Which statement about regular polygons is TRUE?
1. a)Only sides need to be equal
2. b)They must have at least 6 sides
3. c)Both sides AND angles must be equal
4. d)Only angles need to be equal
Answer: Both sides AND angles must be equal
A regular polygon requires both conditions: all sides equal AND all angles equal. A rectangle has equal angles but unequal sides, so it's irregular. A rhombus has equal sides but unequal angles, so it's also irregular.
13.
Is a rhombus a regular quadrilateral? Explain your reasoning.
Answer: no
1. How many sides does a rhombus have? 4
2. Are all sides of a rhombus equal? (yes/no) yes
3. Are all angles of a rhombus equal? (yes/no) no
4. For a polygon to be regular, what must be true? both equal
5. Is a rhombus regular? (yes/no) no
14.
Order these polygons from fewest to most sides: octagon, triangle, hexagon, pentagon, quadrilateral.
Answer: triangle, quadrilateral, pentagon, hexagon, octagon
1. How many sides does a triangle have? 3
2. How many sides does a quadrilateral have? 4
3. How many sides does a pentagon have? 5
4. How many sides does a hexagon have? 6
5. How many sides does an octagon have? 8
6. Now order them: 3, 4, 5, 6, 8 - which polygon has 3 sides? triangle
15.
What is the minimum number of sides a polygon can have?
Answer: 3
A polygon needs at least 3 sides (a triangle). With only 2 straight lines, you cannot create a closed shape - the lines would either be parallel (never meet) or would just create an angle, not a closed figure.