Represent 3D Figures with Nets

Students recognize and draw nets for 3D figures (rectangular prisms, triangular prisms, pyramids) and use nets to find surface area by summing the areas of all faces. They match nets to the 3D shapes they represent and explain how each face of the net corresponds to a face of the solid.

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Grade 6 · Geometry: Area and Surface Area · question 1 of 3

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20 rungs. A star at the top.

This net shows a tent shaped like a pyramid. Counting its floor, how many faces will the tent have?

Your answer:

How it is taught

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A net is the unfolded faces of a solid.

Each face on the net is one face of the solid.

Read it: Surface area from a net

A 5 by 3 by 2 box unfolds into 6 rectangles in 3 matching pairs: two of 5 × 3 = 15, two of 5 × 2 = 10 and two of 3 × 2 = 6. One of each pair is 15 + 10 + 6 = 31, so the surface area is 2 × 31 = 62 square units.

Unfold the box: each face is one rectangle in the net.
Find one rectangle of each matching pair, and add them.
Double it, because every pair has 2 faces.

Top and bottom, front and back, and the two ends match, so 3 areas cover all 6 faces.

A cube's 6 faces are all the same square, so its surface area is 6 times one square.

Surface area is what covers the outside, so it adds the faces.

Surface area = 2 × (length × width + length × height + width × height).

Working out the volume instead: 5 × 3 × 2 = 30.

Surface area adds the faces: 2 × (15 + 10 + 6) = 62.

Each square of a cube's net is 7 by 7. Its surface area is ___ square units. — 294. Each square is 7 × 7 = 49, and 6 × 49 = 294.

Surface area of a 4 × 3 × 2 box

Here's a small cardboard box, four units long, three units wide, and two units tall. How much cardboard does it take to make?

Grade 6 · Unfold a rectangular prism into a net to find surface area

We can cut along the edges and lay the box flat. The flat shape is called a net.

Here it is — six rectangles, one for each face of the box.

The top and bottom match. Each is four by three, so twelve square units. Two of them is twenty-four.

The front and back match too. Each is four by two, so eight square units. Two of them is sixteen.

The two side faces are each three by two, so six square units. Two of them is twelve.

Now we add the six face areas: twelve plus twelve plus eight plus eight plus six plus six.

The surface area is fifty-two square units. That's how much cardboard the box needs!

Now you try. Find the surface area of this net. What is the surface area?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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