Polygons and Types of Quadrilaterals
Polygons are 2D closed shapes made from straight line segments. They are named by their number of sides, like a triangle (3) or pentagon (5). A polygon with n sides has interior angles adding up to (n − 2) × 180°, so a quadrilateral (4) totals 360°.
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What is a Polygon?
- A polygon is a 2D closed shape made from straight line segments.
- Tip: shapes that are open, curved, or 3D are not polygons.
Names of Polygons
- Polygons are named by their number of sides.
- For example: triangle (3), quadrilateral (4), pentagon (5), hexagon (6).
Interior Angles of Polygons
- The sum of interior angles depends on the number of sides.
- The formula is (n − 2) × , where n is the number of sides.
What is a Quadrilateral?
- A quadrilateral is a polygon with four sides.
- Parallelograms, rectangles, rhombuses, squares, and trapeziums are all quadrilaterals.
Practice Questions
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What is the general name for a polygon with four sides?
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Polygons are named by how many sides they have: 3 sides is a triangle, 4 sides is a quadrilateral, 5 sides is a pentagon.
Quadrilateral is the general name that covers every four-sided polygon: squares, rectangles, rhombuses, kites and trapeziums are all quadrilaterals.
True or False: A circle is a polygon.
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A polygon is a closed 2-D shape made only from straight sides that meet at vertices.
A circle's boundary is a single curve with no straight sides and no vertices, so a circle is not a polygon. The statement is False.
Which quadrilateral has all four sides of equal length but no right angles?
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A rhombus has four equal sides, with opposite sides parallel and opposite angles equal, but its angles are not right angles (two are acute and two are obtuse).
A square also has four equal sides, but all of its angles are right angles, so it does not fit the second condition.
What do you call a quadrilateral with opposite sides parallel and all angles at right angles?
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A rectangle is a quadrilateral with both pairs of opposite sides parallel and equal, and all four angles equal to .
A parallelogram also has opposite sides parallel, but its angles are not right angles, so 'parallelogram' alone does not describe this shape.
What is the sum of the interior angles of a pentagon (5-sided polygon)?
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A polygon with n sides splits into triangles from one vertex, and each triangle contributes , giving the formula .
For a pentagon, , so the sum is .
If a polygon has an interior angle sum of , how many sides does it have?
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Use .
Divide both sides by : .
Add 2 to both sides: .
The polygon has 7 sides (a heptagon). Check: . ✓
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Interactive Activity
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Polygons and Types of Quadrilaterals frequently asked questions
The questions students bump into most on this topic
A polygon has at least three straight sides. Three is the minimum, because fewer sides cannot join up to enclose a space. There is no upper limit, and the number of sides gives the polygon its name: three sides make a triangle, four make a quadrilateral, and five make a pentagon.
No, a circle is not a polygon. A polygon must be bounded only by straight line segments, but a circle has a single curved boundary with no straight sides at all. Because that boundary curves instead of running straight, a circle does not meet the definition of a polygon.
The interior angles of a quadrilateral always add up to 360°. A quadrilateral has four sides, so n = 4 in the formula (n − 2) × 180°. Putting in n = 4 gives 360°. This holds for every four-sided shape, including squares, rectangles, parallelograms and trapeziums.
Yes, a square is a special type of rectangle. A rectangle has four right-angled corners, and a square has four right-angled corners too. A square adds one extra condition: all four sides must be equal. So every square is a rectangle, but not every rectangle is a square.
A trapezium has at least one pair of parallel sides, while a parallelogram has two pairs of parallel sides. Because both of a parallelogram's opposite sides are parallel, it also satisfies the trapezium rule. This makes every parallelogram a special type of trapezium, but not every trapezium a parallelogram.