Grade 6 Math Exploring 2D and 3D Shapes

Which of the following is a property of all parallelograms?

• All sides are equal in length.

• Opposite sides are parallel and equal in length.

• All angles are right angles.

• It has exactly one pair of parallel sides.

Answer explanation

In all parallelograms, opposite sides are always parallel and equal in length. This is a defining property, while the other options do not apply to all parallelograms.

Tags

CCSS.HSG.CO.C.11

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

Answer explanation

The sum of the interior angles of a triangle is always 180 degrees. This is a fundamental property of triangles in Euclidean geometry, making the correct answer 180°.

Tags

CCSS.8.G.A.5

Which of the following shapes is a quadrilateral?

• Triangle

• Pentagon

• Rectangle

• Hexagon

Answer explanation

A quadrilateral is a shape with four sides. Among the options, a rectangle has four sides, making it a quadrilateral. A triangle has three sides, a pentagon has five, and a hexagon has six.

Tags

CCSS.2.G.A.1

How many faces does a cube have?

• 4

• 6

• 8

• 12

Answer explanation

A cube has 6 faces, each of which is a square. This is a fundamental property of cubes, distinguishing them from other polyhedra.

Tags

CCSS.6.G.A.4

Which of the following is a property of a regular hexagon?

• All sides are equal, but angles are different.

• All angles are equal, but sides are different.

• All sides and angles are equal.

• It has five sides.

Answer explanation

A regular hexagon has all sides and angles equal, making it a regular polygon. The correct choice is 'All sides and angles are equal.' The other options incorrectly describe the properties of a hexagon.

Tags

CCSS.2.G.A.1

What is the name of a 3D shape with a circular base and a single vertex?

• Cylinder

• Cone

• Sphere

• Pyramid

Answer explanation

A cone is a 3D shape characterized by a circular base and a single vertex (the apex). In contrast, a cylinder has two circular bases, a sphere has no vertices, and a pyramid has a polygonal base with multiple vertices.

Tags

CCSS.1.G.A.1

CCSS.2.G.A.1

Which of the following shapes has exactly one pair of parallel sides?

• Square

• Rectangle

• Trapezoid

• Rhombus

Answer explanation

A trapezoid is defined as a shape with exactly one pair of parallel sides, while a square, rectangle, and rhombus have two pairs of parallel sides. Therefore, the correct answer is trapezoid.

Tags

CCSS.4.G.A.2

How many edges does a rectangular prism have?

• 6

• 8

• 10

• 12

Answer explanation

A rectangular prism has 12 edges. Each of the 6 faces contributes 4 edges, but each edge is shared between 2 faces, resulting in a total of 12 unique edges.

Tags

CCSS.6.G.A.4

What is the term for a polygon with eight sides?

• Hexagon

• Heptagon

• Octagon

• Nonagon

Answer explanation

A polygon with eight sides is called an octagon. The other options are incorrect: a hexagon has six sides, a heptagon has seven sides, and a nonagon has nine sides.

Tags

CCSS.2.G.A.1

Which of the following is a property of a sphere?

• It has edges and vertices.

• It has a flat surface.

• It is perfectly symmetrical around its centre.

• It has a circular base.

Answer explanation

A sphere is defined as a perfectly symmetrical object around its center, meaning all points on its surface are equidistant from the center. The other options describe properties of different shapes, not a sphere.

Tags

CCSS.1.G.A.1

CCSS.2.G.A.1