Depth · one concept from first principles · step 2 of 4
Cut an edge to unroll the sides into one rectangle
In the net of the rectangular prism at the right, rectangle ABCD has an area of . How long is segment AB, in ?
Geometry
Your answer
How to solve
Strategy Draw a Diagram — Unrolled, the four side faces are one rectangle whose width is the whole way round the base. That gives the width without measuring, and the area then hands back the height.
1STEP 1
Find the width of the unrolled rectangle
Going along the row of side faces is going once around the base, so the width is the base's perimeter.
(8 + 5) × 2 = 26
The rectangle is 26 cm wide.
6.G.A.4Draw A DiagramThe four side faces laid in a row are wide.
Why?
Rolled up, that row wraps exactly once round the base, so each point along its width meets one point of the base's outline and the two lengths match.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
Why?
Going round the base once passes the side twice and the side twice, and those four pieces add to the way round.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
2STEP 2
Get the height from the area
Area is width times height, so divide the area by the width just found.
104 ÷ 26 = 4
The prism is 4 cm tall.
6.G.A.1Work Backwards3STEP 3
Match that to segment AB
In the net, AB runs down the short side of the long rectangle, which is the prism's height.
AB = 4
AB is 4 cm.
6.G.A.4Identify SubproblemsAnswer
4 cm
Multiply back: 26 × 4 = 104 cm², the area given.
Takeaway
Unrolled side faces make one rectangle whose width is the whole way round the base.
- Find the width of the unrolled rectangle
- Get the height from the area
- Match that to segment AB
Where next?
Another one like thissuggested
Step back and solidifysuggested
A parent dashboard for the family lives at sensimlab.com.
The same shape shows up later on the AMC, as Net Folding / Face Adjacency. Why the shapes repeat →