Constructions, nets and solids · Construções, malhas e sólidos
| English | Português |
|---|---|
| edge/edʒ/ | aresta |
| scale drawing/skeɪl ˈdrɔːɪŋ/ | desenho em escala |
| net/net/ | líquida |
| face/feɪs/ | face |
| prism/ˈprɪzəm/ | prisma |
| pyramid/ˈpɪrəmɪd/ | pirâmide |
Building with ruler and compasses
- Ancient Greek geometers built every shape using just a straight edge 棱 and compasses — no rulers with markings, no protractors.
- Today, construction questions test whether you can use these tools precisely and leave your working visible.
Construction and solid lab · Laboratório de construção e sólido
Classify geometry tasks by the tool or representation needed. · Classifique tarefas de geometria pela ferramenta ou representação necessária.
Constructing triangles
- To construct a triangle from three sides:
- 1. Draw the base with a ruler.
- 2. Set compasses to the second side length and swing an arc from one end.
- 3. Set compasses to the third side and swing from the other end.
- 4. The intersection is the third vertex. Leave the arcs showing.
Don't erase the arcs. The examiner needs to see your construction arcs to award marks. They prove you used compasses, not guesswork.
To construct a triangle from three given sides you mainly use a ruler and: · Para construir um triângulo a partir de três lados dados, você usa principalmente uma régua e:
Compasses swing arcs of the correct length for the other two sides. · Compassos traçam arcos do comprimento correto para os outros dois lados.
You should erase your construction arcs to keep the drawing neat. · Você deve apagar seus arcos de construção para manter o desenho limpo.
Leave construction arcs visible — the examiner needs to see them to award marks. · Deixe os arcos de construção visíveis — o examinador precisa vê-los para atribuir notas.
Scale drawings · Desenhos em escala 比例图
- A scale drawing represents a real object at a fixed ratio (e.g. $1\text{ cm}:5\text{ m}$).
- Measure on the drawing, then multiply by the scale factor to get the real measurement.
Scale $1:200$. A room measures $3.5\text{ cm}$ on the plan. Real length $= 3.5 \times 200 = 700\text{ cm} = 7\text{ m}$.
A scale drawing uses 1:200. A room measures 3.5 cm on the plan. What is the real length in metres? · Um desenho em escala usa 1:200. Uma sala mede 3,5 cm no plano. Qual é o comprimento real em metros?
3.5 × 200 = 700 cm = 7 m. · 3,5 × 200 = 700 cm = 7 m.
Nets 展开图 and solids
- A net · líquida is a flat shape that folds up into a 3D solid — handy for surface area.
- Face 面: a flat side. Edge: where two faces meet. Vertex · Vértice: a corner.
- A cube has $6$ faces, $12$ edges, and $8$ vertices.
A flat shape that folds up into a solid is called a ______. · Uma forma plana que se dobra para formar um sólido é chamada de ______.
A net is the unfolded, flat version of a solid. · Uma malha é a versão desdobrada e plana de um sólido.
How many faces does a cube have? · Quantas faces um cubo tem?
A cube has 6 square faces (12 edges, 8 vertices). · Um cubo tem 6 faces quadradas (12 arestas, 8 vértices).
How many edges does a cube have? · Quantas arestas um cubo tem?
A cube has 12 edges (where two faces meet). · Um cubo tem 12 arestas (onde duas faces se encontram).
Naming solids
| Solid · Sólido | Key property |
|---|---|
| cube / cuboid | box shapes (all flat faces) |
| prism 棱柱 | same cross-section all along |
| cylinder | circular prism |
| pyramid 棱锥 | comes to a point (apex) |
| cone | circular pyramid |
| sphere | perfectly round |
Coordinate grids help with accurate constructions — shapes can be placed, measured, and transformed precisely.
Use a net to calculate
- A $3\times2\times1$ cm cuboid needs two faces of each size $3\times2$, $3\times1$, $2\times1$. Surface area $S=2(6+3+2)=22\text{ cm}^2$; volume $V=3(2)(1)=6\text{ cm}^3$.
- A triangular prism net has two identical triangles and three rectangles. Their widths match the three triangle sides, and each rectangle length matches the prism length.
A cuboid is 3 cm by 2 cm by 1 cm. Find its surface area in cm². · Um paralelepípedo tem dimensões 3 cm × 2 cm × 1 cm. Encontre sua área superficial em cm².
There are two faces of each size: 2(6+3+2) = 22 cm². · Há duas faces de cada tamanho: 2(6+3+2) = 22 cm².
A rhombus from two triangles
- Draw a 6 cm diagonal AB. Draw 5 cm radius arcs from A and B above and below it, meeting at C and D. Join A-C-B-D-A: all four edges are 5 cm, so the shape is a rhombus. Keep the arcs.
- For a square-based pyramid net, draw a square with one triangle attached to each edge. A base of side 4 cm and face height 3 cm has $S=b^2+4(bh/2)=16+24=40\text{ cm}^2$. Current Core and Extended construction outcomes do not require bisector constructions.
You've got it
- construct with ruler + compasses; leave the construction arcs
- a net · líquida folds into a solid (good for surface area)
- a cube: $6$ faces, $12$ edges, $8$ vertices