Shapes and solids · Grade 4
In Grade 4 you learn: regular and irregular polygons.
Shapes are everywhere: in buildings, packaging, road signs and nature. A 2D shape is flat and is named by its number of sides; a 3D solid takes up space and is described by its faces, edges and vertices (corners).
Key facts
- Triangle 3 sides, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, decagon 10.
- A polygon has as many vertices (corners) as sides.
- Faces are flat surfaces, edges are where two faces meet, vertices are corners.
- A cube and a cuboid each have 6 faces, 12 edges and 8 vertices.
- A prism has the same cross-section all the way along; a pyramid comes to a point (apex).
- For solids with flat faces: faces + vertices − edges = 2 (Euler’s rule).
Worked examples
Example 1
What is the name of this shape, and how many vertices (corners) does it have?
Answer: A hexagon, with 6 vertices.
Example 2
How many faces, edges and vertices does a triangular prism have?
Answer: 5 faces, 9 edges, 6 vertices
Example 3
A prism has ends that are octagons. How many edges does it have?
Answer: 24 edges