Draw a net with appropriate measurements that can be folded into a regular tetrahedron. Verify if it works by making an actual cutout.

Question

Homi · Accepted Answer

A net for a regular tetrahedron is made of four equilateral triangles joined together.

Step 1 — Understanding a Regular Tetrahedron

A regular tetrahedron is a special 3D shape. It has four faces, which are its flat surfaces. Each face is an equilateral triangle. This means all sides of each face are equal. Also, all the edges of the tetrahedron itself are equal in length.

Step 2 — Designing the Net

To make a net, we imagine unfolding the tetrahedron flat onto a surface. If we choose one equilateral triangle as the base, the other three faces must attach to its sides. When we fold these three outer triangles upwards, they will meet at a single point. This point forms the top corner, or apex, of the tetrahedron. The most common net for a regular tetrahedron looks like one large equilateral triangle. This large triangle is divided into four smaller, identical equilateral triangles.

Step 3 — Choosing Measurements

We need to pick a suitable size for our net. Let's choose a size that is easy to draw and cut out. We will make the side length of the final tetrahedron 3 cm. This means each of the four small equilateral triangles in our net will have sides of 3 cm. So, the large equilateral triangle that forms the entire net will have a side length of $2 \times 3 \text{ cm}$ .

$2 \times 3 \text{ cm}$

$\boxed{6 \text{ cm}}$

Therefore, the large equilateral triangle we draw must have a side length of 6 cm.

Step 4 — Drawing the Net

First, draw an equilateral triangle. Make sure each side of this triangle is 6 cm long. Use a ruler to measure the sides accurately. Use a protractor to ensure each angle is 60 degrees. Next, find the midpoint of each of the three sides of this large triangle. Mark these midpoints clearly with a pencil. Now, connect these three midpoints using dotted lines. These dotted lines show where you will fold the paper. The outer edges of the large 6 cm triangle are where you will cut the paper. This drawing is the complete net for the regular tetrahedron.

Diagram 1

Step 5 — Verifying the Net

Carefully cut out the large equilateral triangle along its solid outer edges. Now, gently fold the paper upwards along the three dotted lines (DE, EF, and FD). You will see that the three outer triangles rise up and meet perfectly at a single point. This forms a 3D regular tetrahedron. Each edge of this tetrahedron will measure 3 cm long.

Answer

Draw an equilateral triangle with a side length of 6 cm. Mark the midpoints of each side of this triangle. Connect these midpoints using dotted lines. The outer edges of the 6 cm triangle are the cut lines. The dotted lines are the fold lines. When folded, this net forms a regular tetrahedron with each edge measuring 3 cm. To verify, cut out the net and fold it along the dotted lines.

Question 12

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