Ready to unlock angles, curves, and polygons? Our free geometric shapes quiz is your chance to level up geometry skills with a fun geometry quiz online. From shapes identification quiz tricks for circles and triangles to a complete geometric shapes test covering polygons, you'll tackle essential basic geometry questions and get instant feedback to learn on the go. Jump in to explore key shapes and formulas of geometry and conquer our special quadrilateral quiz. Perfect for students and math buffs, this challenge sharpens your mind and builds confidence. Dive in and start the quiz today!
Easy
How many sides does a pentagon have?
6
7
5
4
A pentagon is a five-sided polygon. The prefix "penta-" means five in Greek. This is one of the most basic polygon definitions used in geometry. Learn more.
What is the sum of the interior angles of a triangle?
180°
360°
270°
90°
The sum of interior angles in any triangle is always 180°. This is a fundamental property in Euclidean geometry and holds for all triangles. Source.
What shape has four equal sides and four right angles?
Rectangle
Rhombus
Parallelogram
Square
A square is the only quadrilateral with four equal sides and four right angles. Rectangles have right angles but not necessarily equal sides. Rhombuses have equal sides but not right angles. Source.
What is the name of a polygon with eight sides?
Hexagon
Heptagon
Octagon
Nonagon
A polygon with eight sides is called an octagon. The prefix "octa-" denotes eight in Greek. Source.
The radius of a circle is half of what?
Perimeter
Area
Circumference
Diameter
The radius is defined as half the diameter of a circle. The diameter spans the full width of the circle through its center. Source.
How many diagonals does a quadrilateral have?
1
3
2
4
A quadrilateral has two diagonals connecting opposite vertices. Using the formula n(n-3)/2 for n=4 gives 4*1/2 = 2 diagonals. Source.
What type of triangle has all sides equal?
Isosceles
Equilateral
Scalene
Right
An equilateral triangle has three equal sides and three equal angles. It is the only triangle where all sides are congruent. Source.
What is the perimeter of a square with side length s?
s
s^2
2s
4s
The perimeter of a square is the sum of its four equal sides, which equals 4 times the side length. Source.
Medium
What is the formula for the area of a circle?
?d²
2?r
?r²
2r²
The area of a circle is ? times the square of its radius. This formula is derived from calculus or by approximating the circle with many-sided polygons. Source.
In a right-angled triangle, which theorem relates the lengths of the sides?
Fermat's theorem
Pythagorean theorem
Thales' theorem
Ceva's theorem
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. It is fundamental in Euclidean geometry. Source.
What is the sum of the interior angles of a hexagon?
720°
540°
360°
900°
The interior angle sum of an n-gon is (n-2)*180°. For a hexagon (n=6), that is 4*180 = 720°. Source.
How many sides does a decagon have?
12
10
9
8
A decagon is a ten-sided polygon; the prefix "deca-" means ten. Source.
What is the measure of each exterior angle of a regular pentagon?
72°
90°
60°
45°
Each exterior angle of a regular n-sided polygon is 360°/n. For a pentagon, 360/5 = 72°. Source.
How many diagonals does a regular hexagon have?
12
9
15
6
A hexagon has n(n-3)/2 diagonals. For n=6, that's 6*3/2 = 9 diagonals. Source.
What is the area of a rectangle with length l and width w?
l + w
2lw
2(l + w)
l × w
The area of a rectangle is the product of its length and width. This formula applies to all rectangles. Source.
In an isosceles triangle, how many sides are equal?
One
None
Three
Two
An isosceles triangle has exactly two equal sides and the base angles opposite those sides are equal. Source.
Hard
What is the length of a diagonal of a rectangle with sides a and b?
a + b
?(a² + b²)
ab
2(a + b)
By the Pythagorean theorem, the diagonal d of a rectangle satisfies d² = a² + b², so d = ?(a² + b²). Source.
What is the sum of the interior angles of a 12-sided polygon?
1800°
2160°
1920°
1440°
The interior angle sum of an n-gon is (n-2)×180°. For n=12, (12-2)×180 = 1800°. Source.
Which formula gives the number of sides n of a regular polygon if each interior angle measures A degrees?
n = 360/A
n = 360/(180 - A)
n = A/(180 - A)
n = 180/(A - 360)
For a regular polygon, interior angle A = 180×(n-2)/n. Solving for n gives n = 360/(180 - A). Source.
What is the area of a regular hexagon with side length a?
(3?3/2)a²
2?3 a²
(?3/4)a²
6a²
A regular hexagon can be divided into 6 equilateral triangles, each of area (?3/4)a², so total area = 6×(?3/4)a² = (3?3/2)a². Source.
An inscribed angle that intercepts a semicircle measures what?
120°
45°
90°
60°
An inscribed angle that subtends a diameter (semicircle) is a right angle (90°) by Thales' theorem. Source.
What is the measure of each interior angle of a regular octagon?
How many lines of symmetry does a regular heptagon have?
6
5
8
7
A regular n-sided polygon has n lines of symmetry. For a heptagon (7 sides), there are 7 lines of symmetry. Source.
What is the area of a trapezoid with bases a and b and height h?
((a + b)/2)h
(a + b)h
2(a + b)h
(a - b)h/2
The area of a trapezoid is the average of the two bases times the height: ((a + b)/2) × h. Source.
Expert
What is the measure of each interior angle of a regular nonagon?
160°
140°
132°
120°
For a regular nonagon (9 sides), each interior angle equals (n-2)×180°/n = 7×180/9 = 140°. Source.
How many diagonals does a 12-sided polygon (dodecagon) have?
48
54
66
60
The number of diagonals in an n-sided polygon is n(n-3)/2. For n=12, that is 12×9/2 = 54. Source.
What is the side length of a regular hexagon inscribed in a circle of radius r?
r/2
2r
?2·r
r
A regular hexagon inscribed in a circle has each side equal to the circle's radius. This follows from dividing the circle into six equilateral triangles. Source.
What is the area of a regular octagon with side length a?
a²(1+?2)/2
a²(2+?2)
4a²(1+?2)
2a²(1+?2)
The area of a regular octagon is 2a²(1+?2). This can be derived by splitting it into eight isosceles triangles or by a known closed-form formula. Source.
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Hard2/8
Expert1/4
AI Study Notes
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Study Outcomes
Identify basic geometric shapes -
After completing the geometric shapes quiz, you will confidently recognize and name circles, triangles, and various polygons in a shapes identification quiz context.
Differentiate angle types -
You'll distinguish between acute, right, and obtuse angles in both simple and complex figures during this geometry quiz online.
Classify polygons by sides -
Learn to categorize polygons based on side count and regularity, enhancing your skills in a geometric shapes test scenario.
Calculate area and perimeter -
Apply basic formulas to compute areas and perimeters of two-dimensional figures using common measurement techniques.
Apply circle properties -
Use definitions of radius, diameter, and circumference to solve problems in this basic geometry questions format.
Enhance problem-solving speed -
Sharpen your critical thinking to quickly answer questions in a fast-paced shapes identification quiz or geometry quiz online.
Cheat Sheet
Circle Fundamentals -
Review the area (A=πr²) and circumference (C=2πr) formulas to conquer any circle question in your geometric shapes quiz. Use the mnemonic "Pie Are Square" for πr² and "All Rabbits Run" for 2πr to lock them into memory. Practicing a few radius-to-diameter conversions solidifies recall for any geometry quiz online.
Triangle Types and Pythagorean Theorem -
Memorize how to classify triangles by sides (equilateral, isosceles, scalene) and angles (acute, right, obtuse); then apply the Pythagorean theorem a²+b²=c² to verify right triangles. A handy trick is the 3-4-5 rule: if sides match this ratio, you have a perfect right triangle. Mastering these basics is vital for any shapes identification quiz and basic geometry questions.
Interior Angle Sum of Polygons -
Use the formula (n - 2)×180° to find the sum of interior angles for an n-sided polygon, such as (5 - 2)×180°=540° for a pentagon. Remember "Start at Two" to subtract two from the number of sides before multiplying. This rule is a cornerstone of your geometric shapes test and simplifies polygon angle problems.
Regular vs. Irregular Polygons and Symmetry -
Regular polygons have all sides and angles equal, leading to consistent lines of symmetry; for example, a regular hexagon boasts six symmetry axes. Irregular polygons lack this uniformity, so look for unequal lengths or angles to spot them quickly. Recognizing symmetry helps you breeze through any geometry quiz online or shapes identification quiz.
Angle Relationships: Complementary, Supplementary, and Vertical -
Complementary angles sum to 90°, supplementary to 180°, and vertical angles are congruent when two lines intersect, making them common in basic geometry questions. Try the rhyme "Comp to Ninety, Sup stays Straight" to recall these definitions instantly. Mastering these angle relationships sharpens your skills for any geometric shapes quiz.
