Problem
A segment in the net is an edge of the solid
A triangular prism is unfolded, and part of the net is hatched. We need the distance around that hatched part.
Geometry
Your answer
How to solve
Strategy Draw a Diagram — Walk the outline and name each piece by the edge of the solid it came from. The two fold lines where the triangles meet the rectangle are inside the region, so they never get counted.
1STEP 1
Match the net's segments to the solid's edges
Every segment in a net is an edge of the solid laid flat, so its length is already given: 12, 7 or 9 for a base edge, 10 for an upright.
12, 7, 9, 10
No new lengths appear in a net.
6.G.A.4Draw A DiagramEvery length in the net is a length on the solid.
Why?
The net is the solid unfolded, and unfolding only turns each face about a crease, which slides and flips it without stretching anything.
🧱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).
2STEP 2
Find which segments are inside the region
Each triangle folds onto a 12 cm edge of the hatched rectangle, so those two 12 cm lines are creases inside the region, not boundary.
12, 12 → inside
The two 12 cm lines are creases, not boundary.
6.G.A.4Visualize Spatial Relationships3STEP 3
Walk the outside boundary
Going round: two free sides of the upper triangle, one upright of the rectangle, two free sides of the lower triangle, the other upright.
7 + 9 + 10 + 7 + 9 + 10
Six edges make the outline.
6.G.A.1Identify Subproblems4STEP 4
Add them
Group the matching pairs to keep the addition easy.
(7 + 9) × 2 + 10 × 2 = 32 + 20 = 52
The perimeter is 52 cm.
6.G.A.1Identify SubproblemsAnswer
52 cm
Sanity check: if the two 12 cm creases had been counted as well, the total would be 76 -- so leaving them out is what the word 'perimeter' asks for.
Takeaway
A crease inside a shape is not part of its outline -- only what you would walk along counts.
- Match the net's segments to the solid's edges
- Find which segments are inside the region
- Walk the outside boundary
- Add them