St. James 02-07-025 Polyhedrons SA, LS

Exploring Three Dimensional Shapes

​Take out spiral to write notes

Open Ended

Which one doesn't belong?

Choose ONE. Write your reasoning as a complete sentence.

Really Pay Attention

The language might be tricky sometimes, or the labeling on the shape might be a little different than what is expected. You need to pay attention to what it is you are looking at. If you do, you'll be able to solve any of these problems with ease. It's all multiplication and addition- just make sure you put the right numbers in the right place.

Know this stuff cold.

Identify Polygons

The term polygon is derived from a Greek word meaning many angles.

Polyhedrons

A polyhedron is a 3D figure that is formed by polygons.

Examples of polyhedrons include a cube, prism, or pyramid.
Non-polyhedrons are cones, spheres, and cylinders because they have sides that are not polygons.

Symbols used in this unit

Multiple Choice

A shape that has 2 dimensions (such as width and height) and no thickness

• 2-Dimensional

• 3-Dimensional

• Polygon

• Polyhedron

Multiple Choice

An object that has 3 dimensions- height, width, and depth (thickness), like any object in the real world.

• Polygon

• Polyhedron

• 3-Dimensional

• 2-Dimensional

Drag and Drop

A ​

Placeholder

is a space figure, or three-dimensional figure, whose surfaces are polygons.  

Drag these tiles and drop them in the correct blank above

polyhedron

cone

cyinder

cylinder

Prisms vs. Pyramids

A prism is a polyhedron with two congruent bases and the lateral sides are rectangles.

A pyramid is a polyhedron with one base and all the lateral sides meet at a common vertex.

Note: All prisms and pyramids are named by their bases.

Prisms are unique in that their formula changes depending on their base. We also name our prisms by the shape of the base. For example, if the base of the prism is a pentagon, then we call it a Pentagonal Prism. Cubes are a special prism in that all six faces are exactly the same square.

Prisms are 3D shapes connected by two similar polygons.

For our purposes, we will use Right Prisms, meaning the two bases will be congruent and not have a slant.

For pyramids, the formula changes according to the base shape, which also determines the name.

For example, if the bottom of the pyramid is a square, we call it a Square Pyramid.

Pyramids are 3D shapes that have one polygonal base that connects to an apex (point at the top).

Pyramids

Circles are not polygons and thus have different shapes on their own.

​
Cylinders are two circles as the bases, which are then connected.
We will be using Right Cylinders, so there is no slant.

Cones have a base, a circle connecting up to an apex. That's what we put ice cream in.

Spheres are... well, balls.

The Circle Ones

Drag and Drop

A ​

Placeholder

is a polyhedron with two congruent, parallelfaces.

Drag these tiles and drop them in the correct blank above

prism

similar solid

sphere

Drag and Drop

A ​

Placeholder

is solid that has two congruent parallel basesthat are circles.

​

Drag these tiles and drop them in the correct blank above

cylinder

polyhedron

pyramid

Drag and Drop

A ​

Placeholder

is polyhedron in which the base is a polygonand the other faces (the lateral faces) are

triangles that meet at a common vertex.

​

Drag these tiles and drop them in the correct blank above

pyramid

polyhedron

cone

Drag and Drop

A ​

Placeholder

is a solid that has one base that is a circle anda vertex that is not on the base.

​

Drag these tiles and drop them in the correct blank above

cone

polyhedron

pyramid

Drag and Drop

A ​

Placeholder

is the set of all points in a space equidistantfrom a given point called the center.

Drag these tiles and drop them in the correct blank above

sphere

surface area

cylinder

cone

Match

Choose the geometric solids to model each object?

cylinder

triangular prism

cylinder & spheres

cylinder & cone

octagonal prism

• cylinder

• triangular prism

• cylinder & spheres

• cylinder & cone

• octagonal prism

Multiple Choice

The intersection of a pair of faces in a three dimensional figure

• Edge

• Face

• Vertices

• Net

Multiple Choice

One of the polygons that makes up a polyhedron

• Edge

• Face

• Net

• Lateral Faces

Multiple Choice

A polyhedron with two parallel and congruent faces, called bases, and all other faces are parallelograms

• Polygon

• Prism

• Quadrilateral

• Trapezoid

Common Formulas

Note: B = base Area and b = length of the base of an object

​Write the formulas you do not know 'cold' (memorized).

​What is Surface Area?

TOTAL Surface area is the amount of space covering the outside of a 3D shape. It is the sum of each face of a 3D object (sides AND bases).

LATERAL Surface area is the sum of the areas of each face of a 3D object, NOT including the bases (sides only).

In Geometry, we will be looking at the Surface Area
of our fundamental 3D shapes. First, let's name them.

Match

Match the image of the 3D shape with its name.

Prism

Pyramid

Cylinder

Cone

Sphere

• Prism

• Pyramid

• Cylinder

• Cone

• Sphere

Multiple Select

What are the two requirements for a shape to be a prism?

• All faces flat

• All faces curved

• Identical and Perpendicular Sides

• Identical and Parallel Sides

Multiple Choice

What shape is this?

• rectangular prism

• a cereal box

• triangular prism

• cylinder

Open Ended

Is this figure a prism? Explain why or why not?

Open Ended

Is this figure a prism? Explain why or why not?

Labelling

The names of five solid shapes are given. Three of them are drawn. Labeling each shape with its correct name.

Drag labels to their correct position on the image

Cube

Sphere

Cylinder

Cuboid

Triangular Prism

Multiple Choice

An example of a pyramid

Poll

Which of the following are considered cylinders? (choose all that apply)

Open Ended

Is this a picture of a Geometric cone? Why or why not?

​Surface Area Formulas
copy the chart in your notes

​Volume

​IXl
Geometry -
Surface Areas of Prisms, Pyramids, Cylinders and Cones
U3
U4
U5

Polypad – The Mathematical Playground

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