Geometry Problem Solver Is a pentagon a quadrilateral?
No. A quadrilateral is a polygon with exactly four sides; a pentagon has five. The two names sit side by side in the same list and never overlap, because a shape has one side count and only one.
Polygons are named by side count
Every polygon name comes straight from how many sides it has, using Greek or Latin roots: tri for three, quad for four, penta for five, hexa for six. Learning the roots is faster than learning the shapes.
Because the count is a single number, the categories cannot overlap. A shape is a quadrilateral or a pentagon, never both, and never neither if it has four or five sides.
Where the confusion comes from
Inside the quadrilateral family the categories do overlap, and that is what trips people up. A square is also a rectangle, also a parallelogram, also a rhombus. So students learn that shape names can nest, and then apply that expectation one level too high.
The nesting works because those names add conditions on top of four sides: parallel sides, equal sides, right angles. Pentagon adds no condition to quadrilateral; it replaces its defining number.
Polygons by number of sides
| Sides | Name | Interior angles add to |
|---|---|---|
| 3 | Triangle | 180° |
| 4 | Quadrilateral | 360° |
| 5 | Pentagon | 540° |
| 6 | Hexagon | 720° |
| 8 | Octagon | 1080° |
Questions
What shapes are quadrilaterals?
Any four-sided polygon: square, rectangle, parallelogram, rhombus, trapezoid, kite, and irregular four-sided shapes with no special name.
Do a pentagon's angles add to 360°?
No, to 540°. The rule is (n - 2) x 180°, so a pentagon gives 3 x 180 = 540. Only quadrilaterals add to 360°.
Is a pentagon a polygon?
Yes. A polygon is any closed shape made of straight sides, so triangles, quadrilaterals, pentagons and the rest are all polygons.
More geometry reference
Stuck on the actual problem
Photograph it and get the worked solution, step by step, with the theorem named at each one.
