Problem
In a prism net the two congruent faces are the bases
A net is folded into a pencil case. We need the total length of every edge of the finished solid.
Geometry
Your answer
How to solve
Strategy Draw a Diagram — Sort the edges into two kinds before adding: the ones that go round a base, which appear twice, and the upright ones, which appear once per base corner.
1STEP 1
Find the bases in the net
The two congruent triangles are the bases; the rectangles between them are the side faces, and their shared height is the prism's height.
(height) = 13
Triangles are the bases, rectangles the sides.
6.G.A.4Draw A Diagram2STEP 2
Add up one base's edges
Going once round a triangular base covers its three sides.
11 + 6 + 8 = 25
25 cm around one base.
6.G.A.4Identify Subproblems3STEP 3
Count both bases and the upright edges
There are two congruent bases, and one upright edge joins each pair of matching corners -- three of them, each 13 cm.
25 × 2 + 13 × 3 = 50 + 39
Two rounds plus three uprights.
6.G.A.4Visualize Spatial RelationshipsEvery edge of the case is either on a base or an upright between them.
Why?
A prism is two bases joined by one upright at each base corner, so no edge can be anywhere else.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
The triangle has three corners, and each carries exactly one upright, so there are three of them.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
Why?
The two bases are congruent, so the second one repeats the same three side lengths as the first.
🧱Rigid motion preserves length and angleSliding, turning, or flipping a shape lays it exactly onto a copy, so every length and angle stays the same (folding is the flip case).
4STEP 4
Total it
Add the base edges and the upright edges together.
50 + 39 = 89
89 cm of edge in all.
6.G.A.4Identify SubproblemsAnswer
89 cm
A triangular prism has 9 edges, and the count here is 3 + 3 + 3 = 9 -- nothing was missed or added twice.
Takeaway
In a net, the two congruent faces are the bases -- find them and the rest sorts itself out.
- Find the bases in the net
- Add up one base's edges
- Count both bases and the upright edges
- Total it