Master Basic Geometric Figures: Triangles, Quadrilaterals, Circles, and More

Question 1

What is the area of a circle with a radius of 5 units?

Accepted Answer

25π square units

Answer

5π square units

Answer

50π square units

Answer

10π square units

Question 2

Which type of triangle has all three sides of equal length?

Accepted Answer

Equilateral

Answer

Scalene

Answer

Isosceles

Answer

Right

Question 3

What is the name for a line segment that joins two opposing vertices of a quadrilateral?

Accepted Answer

Diagonal

Answer

Median

Answer

Altitude

Answer

Base

Question 4

Which of the following is a regular polygon?

Accepted Answer

Square

Answer

Rectangle

Answer

Trapezoid

Answer

Parallelogram

Question 5

Which of the following is not a property of a trapezoid?

Accepted Answer

Two pairs of parallel sides

Answer

One pair of parallel sides

Answer

Diagonals bisect each other

Answer

Opposite angles are equal

Question 6

What is the equation of a circle with center (0, 0) and radius 2?

Accepted Answer

x² + y² = 4

Answer

x² - y² = 4

Answer

x + y = 4

Answer

x - y = 4

Question 7

State the Pythagorean theorem.

Accepted Answer

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Answer

In a right triangle, the square of the hypotenuse is equal to the difference of the squares of the other two sides.

Answer

In a right triangle, the product of the squares of the other two sides is equal to the square of the hypotenuse.

Answer

In a right triangle, the sum of the squares of the other two sides is equal to the square of the hypotenuse.

Question 8

Which shape has four equal sides and four right angles?

Accepted Answer

Square

Answer

Rectangle

Answer

Rhombus

Answer

Trapezoid

Question 9

Find the area of a circle if its radius is 5 units.

Accepted Answer

25π square units

Answer

5π square units

Answer

10π square units

Answer

15π square units

Question 10

Which characteristic is NOT a property of a regular polygon?

Accepted Answer

Concave vertices

Answer

Equal side lengths

Answer

Equal angles

Answer

Convex shape

Question 11

Which shape has two parallel lines and two non-parallel lines?

Accepted Answer

Trapezoid

Answer

Rhombus

Answer

Parallelogram

Answer

Kite

Question 12

What is the total measure of the interior angles of a hexagon?

Accepted Answer

540°

Answer

720°

Answer

900°

Answer

1080°

Question 13

Which regular polygon has 6 sides?

Accepted Answer

Hexagon

Answer

Heptagon

Answer

Octagon

Answer

Nonagon

Question 14

Triangle ABC has vertices A(0, 3), B(3, 0), and C(0, 0). Triangle A'B'C' is the image of triangle ABC after a rotation transformation. The vertices of triangle A'B'C' are A'(4, 2), B'(1, 5), and C'(5, 1). Describe the rotation transformation that maps triangle ABC to triangle A'B'C'

Accepted Answer

Rotation of 90 degrees clockwise around the origin.

Answer

Rotation of 270 degrees counterclockwise around the origin.

Answer

Reflection across the x-axis.

Answer

Translation 3 units to the right and 4 units up.

Question 15

In a regular hexagon, what is the measure of one exterior angle?

Accepted Answer

120 degrees

Answer

60 degrees

Answer

180 degrees

Answer

240 degrees

Question 16

Which transformation results in a change in shape?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 17

Which of the following is an example of a polyhedron?

Accepted Answer

Cube

Answer

Sphere

Answer

Cone

Answer

Cylinder

Question 18

Which of the following is NOT a defining characteristic of a circle?

Accepted Answer

Contains two parallel chords

Answer

All points are equidistant from the center

Answer

Contains no vertices

Answer

Has a diameter

Question 19

Which of the following is NOT recognized as a type of angle?

Accepted Answer

Convex

Answer

Acute

Answer

Obtuse

Answer

Straight

Question 20

Determine the formula used to calculate the circumference of a circle.

Accepted Answer

2πr

Answer

πr³

Answer

πd

Answer

4πr²

Question 21

What is the formula used to calculate the area of a triangle?

Accepted Answer

A = ½ * base * height

Answer

A = length * width

Answer

A = π * radius²

Answer

A = 4/3 * π * radius³

Question 22

How are polygons differentiated from polyhedrons?

Accepted Answer

Polygons are two-dimensional, while polyhedrons are three-dimensional.

Answer

Polygons have straight sides, while polyhedrons have curved sides.

Answer

Polygons are defined by vertices, while polyhedrons are defined by faces.

Answer

There is no difference between a polygon and a polyhedron.

Question 23

Which three-dimensional shape has all square faces?

Accepted Answer

Cube

Answer

Sphere

Answer

Cone

Answer

Pyramid

Question 24

What is the formula for calculating the volume of a cylinder?

Accepted Answer

V = π * r² * h

Answer

V = 4/3 * π * r³

Answer

V = length * width * height

Answer

V = 1/3 * π * r² * h

Question 25

Which theorem establishes a relationship between the exterior angles of a triangle?

Accepted Answer

Exterior Angle Theorem

Answer

Triangle Sum Theorem

Answer

Pythagorean Theorem

Answer

Law of Cosines

Question 26

What is the name of the point where the medians of a triangle intersect?

Accepted Answer

Centroid

Answer

Circumcenter

Answer

Incenter

Answer

Orthocenter

Question 27

Which of the following is NOT a defining property of a triangle?

Accepted Answer

Two right angles

Answer

Three sides

Answer

Three angles that sum to 180 degrees

Answer

A closed figure

Question 28

What is the specific name for a quadrilateral with four equal sides?

Accepted Answer

Square

Answer

Rectangle

Answer

Parallelogram

Answer

Rhombus

Question 29

Which of the given figures represents a three-dimensional shape?

Accepted Answer

Cube

Answer

Square

Answer

Pentagon

Answer

Circle

Question 30

What is the sum of the interior angles of a pentagon?

Accepted Answer

540 degrees

Answer

360 degrees

Answer

720 degrees

Answer

900 degrees

Question 31

Which of the following is a regular polygon?

Accepted Answer

Square

Answer

Rectangle

Answer

Parallelogram

Answer

Kite

Question 32

What is the formula to calculate the area of a circle?

Accepted Answer

πr²

Answer

πd

Answer

4πr²

Answer

2πr

Question 33

Which of the following is NOT a property of a rectangle?

Accepted Answer

All sides are congruent

Answer

Opposite sides are parallel

Answer

Diagonals are congruent

Answer

Angles are right angles

Question 34

Which shape has 4 equal sides and 4 right angles?

Accepted Answer

Square

Answer

Rectangle

Answer

Trapezoid

Answer

Rhombus

Question 35

Which angle measures more than 90 degrees?

Accepted Answer

Obtuse

Answer

Right

Answer

Acute

Answer

Straight

Question 36

What is the circumference of a circle with a radius of 10 cm?

Accepted Answer

20π cm

Answer

10π cm

Answer

2π cm

Answer

40π cm

Question 37

Which shape is cone-like with a circular base?

Accepted Answer

Cone

Answer

Sphere

Answer

Cylinder

Answer

Pyramid

Question 38

Which of the following statements is NOT true about a parallelogram?

Accepted Answer

All sides are equal.

Answer

Opposite angles are congruent.

Answer

Diagonals bisect each other.

Answer

Opposite sides are parallel.

Question 39

What is the area of a circle with a radius of 5 centimeters?

Accepted Answer

25π cm²

Answer

50π cm²

Answer

10π cm²

Answer

15π cm²

Question 40

Which of the following shapes is a regular polygon?

Accepted Answer

Square

Answer

Parallelogram

Answer

Trapezoid

Answer

Rhombus

Question 41

What is the sum of the interior angles of a triangle?

Accepted Answer

180°

Answer

360°

Answer

270°

Answer

90°

Question 42

What is the volume of a cube with a side length of 3 centimeters?

Accepted Answer

27 cm³

Answer

9 cm³

Answer

18 cm³

Answer

36 cm³

Question 43

A trapezoid has bases measuring 6 centimeters and 8 centimeters, and a height of 4 centimeters. What is its area?

Accepted Answer

28 cm²

Answer

42 cm²

Answer

14 cm²

Question 44

Which of the following is an example of a composite figure?

Accepted Answer

A rectangle with a semicircle attached

Answer

Square

Answer

Triangle

Answer

Circle

Question 45

What is the circumference of a circle with a diameter of 10 centimeters?

Accepted Answer

10π cm

Answer

15π cm

Answer

5π cm

Answer

20π cm

Question 46

Which of these statements is NOT a property of a square?

Accepted Answer

It has 5 sides.

Answer

It has 4 equal sides.

Answer

It has 4 right angles.

Answer

Its diagonals are perpendicular bisectors of each other.

Question 47

What is the measure of each interior angle of a regular hexagon?

Accepted Answer

120 degrees

Answer

90 degrees

Answer

180 degrees

Answer

60 degrees

Question 48

Which of the following describes a key property of a parallelogram?

Accepted Answer

Opposite sides are parallel and equal in length.

Answer

It has a circular base.

Answer

It has five sides.

Answer

All angles are right angles.