Amir cuts open a cardboard box and flattens it into a net. The net he obtains has the following pieces arranged in a strip:
• A rectangle labelled P (8 cm wide, 6 cm tall) on the left
• A rectangle labelled Q (10 cm wide, 6 cm tall) in the middle
• A rectangle labelled R (8 cm wide, 6 cm tall) on the right
Attached to the TOP edge of rectangle Q is an isosceles triangle with a base of 10 cm and two equal slant sides of 8 cm.
Attached to the BOTTOM edge of rectangle Q is an identical isosceles triangle (base 10 cm, slant sides 8 cm).
When Amir folds this net along all the edges, which 3D solid is formed?
ATriangular prism
BRectangular prism
CSquare pyramid
DTriangular pyramid
Show Worked Solution
Worked Solution
Step 1: Count and classify all faces in the net.
Rectangles: P (8 × 6 cm), Q (10 × 6 cm), R (8 × 6 cm) — 3 rectangular faces.
Triangles: one isosceles triangle (base 10 cm, equal sides 8 cm) above Q; one identical triangle below Q — 2 triangular faces.
Total faces: 3 + 2 = 5 faces.
Step 2: Identify which solid has exactly 2 triangular faces and 3 rectangular faces.
Triangular prism: 2 triangular end faces + 3 rectangular lateral faces = 5 faces. ✓
Rectangular prism: 6 rectangular faces. ✗
Square pyramid: 1 square base + 4 triangular faces = 5 faces, but no rectangular faces. ✗
Triangular pyramid: 4 triangular faces = 4 faces, no rectangular faces. ✗
Step 3: Verify the folding makes sense.
The strip P–Q–R folds into the three lateral (side) rectangles wrapping around the length of the prism. The two triangles fold up to close off the two triangular end faces.
Answer: Triangular prism
Correct answer: Triangular prism
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