Your teacher will provide you a drawing of a polyhedron. You will draw its net and calculate its surface area. 

What polyhedron execute you have?

Study your polyhedron. Then, draw its net on graph paper. Usage the side size of a grid square as the unit.

You are watching: The sum of the areas of the faces of a three dimensional figure

Label every polygon on the net v a name or number.

Find the surface ar area of your polyhedron. Display your thinking in an arranged manner so that it can be complied with by others.

Here room the nets of 3 cardboard boxes that are all rectangle-shaped prisms. The boxes will be packed through 1-centimeter cubes. All lengths are in centimeters.



Compare the surface locations of the boxes. Which box will use the the very least cardboard? display your reasoning.Now compare the volumes of this boxes in cubic centimeters. Which crate will organize the many 1-centimeter cubes? show your reasoning.
Figure C reflects a net of a cube. Draw a various net that a cube. Draw one more one. And then another one. How plenty of different nets deserve to be drawn and also assembled into a cube?

The surface ar area of a polyhedron is the amount of the areas of every one of the faces. Due to the fact that a net reflects us all faces the a polyhedron in ~ once, that can assist us uncover the surface area. We can discover the areas of every polygons in the net and include them.





A square pyramid has actually a square and also four triangles for its faces. Its surface area is the amount of the areas of the square base and also the four triangular faces:

\((6\boldcdot 6) + 4\boldcdot \left(\frac12 \boldcdot 5 \boldcdot 6\right) = 96\)

The surface ar area that this square pyramid is 96 square units.

A prism has actually two identical bases that are parallel. A pyramid has actually one base.

A prism or pyramid is called for the shape of that is base.

Description: The number on the left is labeling pentagonal prism. There room two identical pentagons ~ above the top and also bottom. Every vertex the a pentagon is linked by a upright segment to the corresponding vertex that the other pentagons. The pengatons are each shaded, with words base pointing come each. The number on the best is labeled hexagonal pyramid. There is a hexagon on the bottom shaded green. Indigenous a point over the hexagon expand 6 segments, each connected to a crest of the hexagon.

Each flat side of a polyhedron is called a face. For example, a cube has actually 6 faces, and they are all squares.

A polyhedron is a closed, three-dimensional shape with flat sides. Once we have much more than one polyhedron, we call them polyhedra.

A prism is a kind of polyhedron that has two bases that space identical copies of every other. The bases are connected by rectangles or parallelograms.

A pyramid is a kind of polyhedron that has one base. All the other faces are triangles, and they all meet at a single vertex.

The surface ar area of a polyhedron is the variety of square devices that covers all the faces of the polyhedron, without any type of gaps or overlaps.

For example, if the encounters of a cube each have an area the 9 cm2, then the surface ar area that the cube is \(6 \boldcdot 9\), or 54 cm2.

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