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Quizzes > Mathematics

Shapes Quiz: Can You Name Every Shape?

Quick, free geometric shapes quiz with instant feedback and results.

Editorial: Review CompletedCreated By: Chouw Feng RunUpdated Aug 28, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration for shape skills quiz on sky blue background

This shapes quiz helps you recognize and name 2D and 3D figures with clear visuals, hints, and instant feedback as you go. Want to go further? Try our 3d shapes quiz, challenge your knowledge in a polygon test, or review key rules in a quadrilateral properties test.

Which polygon has exactly three sides?
Pentagon
Triangle
Hexagon
Quadrilateral
A triangle is a polygon characterized by exactly three sides and three angles that sum to 180 degrees. It is the simplest form of a polygon in Euclidean geometry. Triangles can be classified by side length or angle measures.
Which shape has four equal sides and four right angles?
Rhombus
Rectangle
Square
Trapezoid
A square is defined as a quadrilateral with four equal sides and four right angles. It is a special type of rectangle and rhombus meeting both sets of criteria. All internal angles are 90 degrees and opposite sides are parallel.
How many sides does a hexagon have?
6
5
8
7
A hexagon is a six-sided polygon. If it is regular, all six sides and angles are equal. Hexagons commonly appear in natural and human-made structures, like honeycombs.
Which three-dimensional shape has six square faces?
Octahedron
Tetrahedron
Cube
Rectangular prism
A cube is a regular hexahedron with six identical square faces. All edges of a cube are equal in length and all angles are right angles. It is one of the five Platonic solids.
Which shape has a circular base and a single vertex?
Pyramid
Cylinder
Cone
Sphere
A cone has a circular base and tapers smoothly to a single vertex called the apex. It has one curved surface and one flat face. This distinguishes it from cylinders and pyramids.
What is the name of the set of points in a plane that are all the same distance from a fixed center?
Parabola
Circle
Hyperbola
Ellipse
A circle is defined as the locus of points equidistant from a single fixed point called the center. That fixed distance is the radius of the circle. Other conic sections have different distance properties.
Which quadrilateral has only one pair of parallel sides?
Trapezoid
Parallelogram
Rectangle
Rhombus
A trapezoid (or trapezium in some regions) is a quadrilateral with exactly one pair of parallel sides. The other two sides are non-parallel. This differentiates it from parallelograms and rectangles.
Which three-dimensional shape has no edges or vertices?
Sphere
Cube
Cylinder
Cone
A sphere has a continuous curved surface with no edges or vertices. Every point on the surface is equidistant from the center. It differs from polyhedral shapes which have flat faces, edges, and vertices.
What is the name of a regular polygon with eight sides?
Heptagon
Octagon
Nonagon
Decagon
An octagon is an eight-sided polygon. In a regular octagon, all sides and interior angles are equal. The sum of interior angles in any octagon is 1080 degrees.
How many edges does a rectangular prism have?
14
12
8
10
A rectangular prism has 12 edges: four along the top, four along the bottom, and four vertical edges. It also has 6 faces and 8 vertices. This shape is a three-dimensional extension of a rectangle.
Which shape is formed by slicing a cylinder with a plane parallel to its base?
Triangle
Ellipse
Rectangle
Circle
When a cylinder is cut by a plane parallel to its circular base, the cross-section is a circle of the same radius. This is because the plane intersects the curved surface in a path equidistant from the axis. Any other orientation can yield different conic sections.
What is the measure of each interior angle in a regular pentagon?
135°
90°
108°
120°
A regular pentagon has five equal sides and five equal interior angles. The formula for each interior angle in a regular n-gon is (n-2)*180/n, which gives (5-2)*180/5 = 108 degrees. This holds for any regular pentagon.
A triangular prism has how many faces total?
7
4
6
5
A triangular prism has two triangular bases and three rectangular lateral faces, totaling five faces. It also has nine edges and six vertices. This shape is a polyhedron with prism symmetry.
Which conic section is defined as the set of all points where the sum of distances to two foci is constant?
Hyperbola
Circle
Ellipse
Parabola
An ellipse is defined as the locus of points for which the sum of distances from two fixed points (foci) is constant. A circle is a special case where the two foci coincide. Hyperbolas and parabolas have different focal definitions.
Which quadrilateral has perpendicular diagonals and two pairs of adjacent equal sides?
Parallelogram
Rhombus
Trapezoid
Kite
A kite is a quadrilateral with two distinct pairs of adjacent sides that are equal, and its diagonals intersect at right angles. One of its diagonals also bisects the other. This distinguishes it from rhombi and parallelograms.
In a right triangle, the side opposite the right angle is called what?
Hypotenuse
Base
Adjacent side
Opposite side
In a right triangle, the hypotenuse is the side opposite the right (90°) angle and is the longest side of the triangle. It is used in the Pythagorean theorem: a² + b² = c². The other two sides are called legs.
How many faces does a regular dodecahedron have?
30
20
10
12
A regular dodecahedron is one of the five Platonic solids and has 12 regular pentagonal faces. It also has 20 vertices and 30 edges. Its symmetry is denoted by the Coxeter group [5,3].
What is the sum of the interior angles of a nonagon (9-sided polygon)?
1080°
1620°
1440°
1260°
The sum of interior angles of any n-sided polygon is (n-2)*180 degrees. For a nonagon, n=9, so (9-2)*180 = 7*180 = 1260 degrees. This formula applies to all simple polygons.
What is the name of the three-dimensional shape created by rotating a right triangle around one of its legs?
Sphere
Torus
Cylinder
Cone
Rotating a right triangle about one of its legs generates a right circular cone. The leg becomes the axis of the cone and the hypotenuse traces the sloping side. Cones have a circular base and a vertex.
Which polyhedron is made up of 20 equilateral triangular faces?
Tetrahedron
Icosahedron
Octahedron
Dodecahedron
An icosahedron is a Platonic solid composed of 20 equilateral triangular faces, 12 vertices, and 30 edges. It has the highest number of faces among the Platonic solids. Its symmetry group is [3,5].
In a regular hexagon, what is the measure of each interior angle?
135°
150°
120°
100°
A regular hexagon has interior angles given by (n-2)*180/n with n=6, yielding (6-2)*180/6 = 120 degrees per angle. All sides and angles in a regular hexagon are congruent. It easily tessellates the plane.
If a pyramid with a square base is cut by a plane parallel to its base, the cross-section is a:
Square
Trapezoid
Triangle
Rectangle
A cross-section of a pyramid by a plane parallel to its base is a smaller, similar polygon to the base. For a square pyramid, this cross-section is also a square. The linear dimensions of the cross-section scale proportionally.
What is the dihedral angle between two adjacent faces of a cube?
120°
45°
90°
60°
A cube has all faces meeting at right angles. The dihedral angle between any two adjacent faces of a cube is therefore 90 degrees. This is a key property of orthogonal polyhedra.
For a convex polyhedron, Euler's formula V - E + F = 2 holds. If a polyhedron has 12 vertices and 20 faces, how many edges does it have?
32
28
30
34
Euler's characteristic for convex polyhedra states V - E + F = 2. Substituting V=12 and F=20 gives 12 - E + 20 = 2. Solving yields E = 30 edges.
Which Platonic solid is the dual polyhedron of the cube?
Octahedron
Icosahedron
Dodecahedron
Tetrahedron
The dual of a cube is an octahedron, where each face of the cube corresponds to a vertex of the octahedron. Duality swaps faces and vertices while preserving connectivity. Both are Platonic solids.
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Study Outcomes

  1. Identify Geometric Figures -

    Pinpoint and name a range of shapes from basic triangles to complex polygons in diverse patterns.

  2. Classify Polygons -

    Group shapes by characteristics such as side count and symmetry to understand polygon families.

  3. Analyze Shape Properties -

    Examine angles, sides, and patterns to distinguish between similar geometric figures.

  4. Apply Visual Recognition Skills -

    Use pattern recognition techniques to quickly spot and identify shapes in various contexts.

  5. Evaluate Quiz Performance -

    Assess your score and pinpoint which shapes need further review to track improvement.

  6. Enhance Spatial Awareness -

    Develop a keener eye for geometric arrangements and improve overall spatial reasoning abilities.

Cheat Sheet

  1. Triangle Classification -

    In any shapes quiz, triangles are sorted by sides (equilateral, isosceles, scalene) and angles (acute, right, obtuse). According to Euclid's Elements and modern sources like Khan Academy, learning these categories speeds up pattern recognition. Use the acronym EIS to recall Equilateral, Isosceles, Scalene quickly during your shapes quiz.

  2. Circle Formulas -

    Essential for any shapes quiz is mastering circle metrics like circumference C=2πr and area A=πr². MathisFun and NASA's educational resources recommend practicing with different radius values to build fluency. Remember that the diameter is always twice the radius (d=2r) for quick checks.

  3. Polygon Angle Relationships -

    For regular polygons, each interior angle measures ((n−2)×180)/n and the total sum is (n−2)×180, as noted by Wolfram MathWorld. For example, a regular hexagon has interior angles of 120° (720°/6). Keep a small chart for n=3 - 12 to ace your shapes quiz.

  4. Symmetry and Transformations -

    Understanding reflection, rotation, and translation helps identify congruence and symmetry in shapes quiz questions. The National Council of Teachers of Mathematics highlights practicing both line and rotational symmetry to improve speed. Visualizing shapes on a coordinate grid strengthens your ability to predict transformation outcomes.

  5. 3D Shape Volumes and Surface Areas -

    In more advanced shapes quiz sections, solid figures require formulas like V=ℓwh for rectangular prisms, V=4/3πr³ for spheres, and V=(1/3)Bh for pyramids (Britannica). Memorizing these with flashcards aligns with strategies from university math syllabi. Always cross-check units: cm³ for volume and cm² for surface area.

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