Geometry for Seventh Graders: Master Shapes and Spaces

Question 1

Which everyday object is shaped like a rectangular prism?

Accepted Answer

Cardboard box

Answer

Car tire

Answer

Soccer ball

Question 2

What is a rotation in two dimensions? Explain how to rotate a shape around a fixed point by a given angle. Include a diagram to illustrate the process.

Accepted Answer

A rotation in two dimensions involves moving a shape in a circular motion around a fixed point, resulting in a congruent shape.

Answer

In a rotation, a shape moves along a straight line, resulting in a shape similar to the original.

Answer

Rotation involves flipping a shape over a line of symmetry.

Answer

Rotation enlarges a shape, resulting in a similar but larger shape.

Question 3

How do geometric shapes and principles contribute to creating visually appealing and meaningful art? Give examples.

Accepted Answer

Geometric shapes, like circles and squares, create balanced and visually pleasing compositions.

Answer

Geometric principles, like symmetry and proportion, are not essential in art and design.

Answer

Geometric elements are only important in modern and abstract art, not traditional or realistic styles.

Question 4

To translate a square with vertices A(0, 0), B(1, 0), C(1, 1), and D(0, 1) three units to the right and two units up, what steps should you take?

Accepted Answer

Add 3 to the x-coordinate and 2 to the y-coordinate of each vertex.

Answer

Subtract 3 from the x-coordinate and 2 from the y-coordinate of each vertex.

Answer

Multiply the x-coordinate by 3 and the y-coordinate by 2 for each vertex.

Answer

Divide the x-coordinate by 3 and the y-coordinate by 2 for each vertex.

Question 5

Which of the properties below does NOT belong to a circle?

Accepted Answer

Has sides

Answer

Has a center point

Answer

Has a radius

Answer

Has a diameter

Question 6

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

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 7

Which of the following is not a type of quadrilateral?

Accepted Answer

Triangle

Answer

Square

Answer

Trapezoid

Answer

Rectangle

Question 8

What is the formula for finding the area of a circle?

Accepted Answer

A = πr²

Answer

A = 2πr

Answer

A = πr³

Answer

A = r²

Question 9

Which of the following is a three-dimensional shape?

Accepted Answer

Sphere

Answer

Triangle

Answer

Rectangle

Answer

Trapezoid

Question 10

Which of the following is NOT a way to classify triangles based on their sides?

Accepted Answer

Acute

Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 11

Which of the following is the most precise way to describe the shape of a baseball?

Accepted Answer

Ellipsoid

Answer

Sphere

Answer

Circle

Answer

Cylinder

Question 12

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

Accepted Answer

Has opposite sides parallel

Answer

Has no corners

Answer

Has a diameter

Answer

Has a perimeter

Question 13

What is the area of a square with a side length of 5 cm?

Accepted Answer

25 cm²

Answer

10 cm²

Answer

20 cm²

Answer

50 cm²

Question 14

Which of the following shapes is a regular polygon?

Accepted Answer

Square

Answer

Triangle

Answer

Rectangle

Answer

Trapezoid

Question 15

What is the volume of a sphere with a radius of 3 cm?

Accepted Answer

18π cm³

Answer

9π cm³

Answer

27π cm³

Answer

36π cm³

Question 16

What is the surface area of a cube with an edge length of 4 cm?

Accepted Answer

64 cm²

Answer

16 cm²

Answer

32 cm²

Answer

96 cm²

Question 17

Which of the following shapes has the greatest perimeter?

Accepted Answer

Square with side length 5 cm

Answer

Rectangle with length 6 cm and width 4 cm

Answer

Triangle with sides 3 cm, 4 cm, and 5 cm

Answer

Circle with radius 2 cm

Question 18

Identify the property that does not belong to a circle:

Accepted Answer

Has four sides

Answer

Possesses a center

Answer

Has a radius

Answer

Has a circumference

Question 19

Name the triangle that has all three sides of equal length.

Accepted Answer

Equilateral triangle

Answer

Isosceles triangle

Answer

Scalene triangle

Answer

Right triangle

Question 20

What is the measure of an angle that is greater than 90 degrees but less than 180 degrees?

Accepted Answer

Obtuse angle

Answer

Acute angle

Answer

Right angle

Answer

Straight angle

Question 21

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This statement is known as the:

Accepted Answer

Pythagorean theorem

Answer

Triangle theorem

Answer

Hypotenuse theorem

Answer

Perpendicular theorem

Question 22

Which of the following is a property of a circle?

Accepted Answer

Has a center point

Answer

Has endpoints called vertices

Answer

Has straight sides

Answer

Does not have a defined shape

Question 23

Which of the following quadrilaterals does NOT have opposite sides parallel?

Accepted Answer

Trapezoid

Answer

Square

Answer

Rectangle

Answer

Rhombus

Question 24

Which of the following is a two-dimensional shape?

Accepted Answer

Triangle

Answer

Cylinder

Answer

Cube

Answer

Sphere

Question 25

Which of the following is a cone?

Accepted Answer

A shape with a circular base and a single vertex

Answer

A shape with two circular bases and a curved surface

Answer

A shape with three or more flat sides

Answer

A shape with a square base and a single vertex

Question 26

Which of the following is a geodesic dome?

Accepted Answer

A dome made up of triangles

Answer

A dome made up of squares

Answer

A dome made up of circles

Answer

A dome made up of hexagons

Question 27

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

Accepted Answer

Infinite number of corners

Answer

Closed curve

Answer

Equal radii from the center

Answer

Constant circumference

Question 28

The area of a square is 36 square inches. What is the length of each side?

Accepted Answer

6 inches

Answer

3 inches

Answer

9 inches

Answer

12 inches

Question 29

Which of the following is a type of quadrilateral?

Accepted Answer

Trapezoid

Answer

Pentagon

Answer

Octagon

Answer

Oval

Question 30

Which of the following is the formula for the surface area of a sphere?

Accepted Answer

4πr²

Answer

πr²

Answer

2πr

Answer

3πr²

Question 31

Which of the following is a characteristic of a circle?

Accepted Answer

Has two radii of equal length

Answer

Has an infinite number of sides

Answer

Has parallel sides

Answer

Has four right angles

Question 32

Which of the following is a three-dimensional shape?

Accepted Answer

Sphere

Answer

Square

Answer

Triangle

Answer

Rectangle

Question 33

Which of the following is a polygon with 6 sides?

Accepted Answer

Hexagon

Answer

Pentagon

Answer

Octagon

Answer

Decagon

Question 34

What makes fractals unique? Choose the answer that best describes their geometric properties and real-world examples.

Accepted Answer

Fractals are irregular shapes that repeat at different sizes, creating self-similarity. You can find them in nature, like snowflakes and ferns.

Answer

Fractals only exist in computer images and have no uses in the real world.

Answer

Fractals are three-dimensional objects that can't be drawn on a flat surface.

Answer

Fractals have no mathematical importance and are just for looks.

Question 35

Which shape has 4 equal sides and 4 right angles?

Accepted Answer

Rectangle

Answer

Trapezoid

Answer

Rhombus

Answer

Parallelogram

Question 36

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

Accepted Answer

25π cm²

Answer

50π cm²

Answer

10π cm²

Answer

40π cm²

Question 37

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

Accepted Answer

It has four sides.

Answer

It has three sides.

Answer

It has three angles.

Answer

The sum of its interior angles is 180 degrees.

Question 38

What is the surface area of a cube with an edge length of 5 cm?

Accepted Answer

100 cm²

Answer

25 cm²

Answer

50 cm²

Answer

150 cm²

Question 39

What is the Pythagorean Theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

a + b = c

Answer

a - b = c

Question 40

Which shape is a regular polygon?

Accepted Answer

Square

Answer

Rectangle

Answer

Trapezoid

Answer

Rhombus

Question 41

Which property is true for a trapezoid?

Accepted Answer

Opposite sides are parallel.

Answer

Has equal diagonals

Answer

Has four right angles

Answer

Is a regular polygon

Question 42

What is the volume of a rectangular prism with a length of 10 centimeters, a width of 5 centimeters, and a height of 4 centimeters?

Accepted Answer

200 cubic centimeters

Answer

20 cubic centimeters

Answer

50 cubic centimeters

Answer

400 cubic centimeters

Question 43

Which shape is three-dimensional?

Accepted Answer

Sphere

Answer

Circle

Answer

Square

Answer

Triangle

Question 44

Calculate the surface area of a cylinder with a radius of 4 cm and a height of 6 cm.

Accepted Answer

96π cm²

Answer

48π cm²

Answer

144π cm²

Answer

288π cm²

Question 45

Which of these three-dimensional shapes has a circular base and a single vertex?

Accepted Answer

Cone

Answer

Sphere

Answer

Cube

Answer

Cylinder

Question 46

Which of these is NOT a property of a circle?

Accepted Answer

Has two parallel sides

Answer

Has a constant radius

Answer

Has a fixed center point

Answer

Has a circumference

Question 47

What is the measure of an angle that is complementary to a 45° angle?

Accepted Answer

90°

Answer

30°

Answer

45°

Answer

60°

Question 48

Which of these is the net for a cylinder?

Accepted Answer

A circle and a rectangle

Answer

Two circles and a rectangle

Answer

A square and a triangle

Answer

A pentagon and a hexagon

Question 49

The Pythagorean theorem states which relationship between the side lengths of a right triangle?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Answer

a + b = c

Question 50

Select the characteristic that is true for triangles?

Accepted Answer

Have exactly three angles

Answer

Have exactly four sides

Answer

Always have sides of equal length

Answer

Have exactly two parallel sides

Question 51

Calculate the area of a square with a side length of 5 cm?

Accepted Answer

25 cm²

Answer

10 cm

Answer

10 cm²

Answer

25 cm

Question 52

Which figure does NOT belong to the quadrilateral category?

Accepted Answer

Pentagon

Answer

Square

Answer

Rectangle

Answer

Trapezoid

Question 53

Which property is characteristic of parallel lines?

Accepted Answer

Never intersect

Answer

Intersect at right angles

Answer

Intersect at any angle

Answer

Always have equal lengths

Question 54

Identify the three-dimensional shape formed when a rectangle is rotated around one of its sides?

Accepted Answer

Cylinder

Answer

Sphere

Answer

Cone

Answer

Prism

Question 55

Which equation represents the formula for finding the area of a trapezoid?

Accepted Answer

A = ½ (b1 + b2)h

Answer

A = πr²

Answer

A = s²

Answer

A = V/h

Question 56

Which quadrilateral has four equal sides and four right angles?

Accepted Answer

Square

Answer

Rhombus

Answer

Rectangle

Answer

Trapezoid

Question 57

Which of the following is NOT a valid method for classifying triangles?

Accepted Answer

By perimeter

Answer

By side length

Answer

By shape

Answer

By angle measure

Question 58

Determine the volume of a rectangular prism with a length of 5 centimeters, a width of 3 centimeters, and a height of 4 centimeters.

Accepted Answer

60 cubic centimeters

Answer

30 cubic centimeters

Answer

45 cubic centimeters

Answer

20 cubic centimeters

Question 59

Which characteristic is unique to circles?

Accepted Answer

All points on the circumference are equidistant from the center.

Answer

Circles have greater area than squares.

Answer

Circles can be divided into equal sectors.

Question 60

Calculate the surface area of a sphere with a radius of 8 centimeters.

Accepted Answer

256π square centimeters

Answer

128π square centimeters

Answer

512π square centimeters

Answer

64π square centimeters

Question 61

Select the statement that represents the Pythagorean theorem:

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Answer

b² - a² = c²

Question 62

Identify a property of a cylinder.

Accepted Answer

It has parallel circular faces.

Answer

It always has square bases.

Answer

Its volume is given by the formula V = πr³.

Answer

Its lateral surface is always flat.

Question 63

Identify the property that is NOT a characteristic of parallelograms:

Accepted Answer

All sides are congruent

Answer

Opposite angles are congruent

Answer

Opposite sides are parallel

Question 64

When a triangle has two equal sides, it is classified as a:

Accepted Answer

Isosceles triangle

Answer

Scalene triangle

Answer

Equilateral triangle