3.1 Area

• Area of a pentagon and a hexagon
• Surface area of triangular and rectangular-based prisms
• Surface area of triangular, rectangular and square-based pyramids, cones and spheres
• Area of a sector and segment of a circle

• calculate the area of a pentagon and a hexagon in different situations
• work out the surface area of triangular and rectangular-based prisms
• work out the surface area of triangular, rectangular and square-based pyramids
• calculate the area of a sector and segment of a circle
• work out the surface area of a cone in real-life situations
• calculate the surface area of a sphere in real-life situations
• recognise the use of area in real-life situations

“How do we work out the area of different surfaces?”

The titles are open to everyone. Reading a lesson needs an account — sign in or create one.

1. Area of a pentagon and a hexagon
   40 min · 1 practice tasks · quiz
   Split a regular polygon into identical triangles from its centre, then multiply one triangle by the number of sides.
2. Nets: opening a solid out flat
   40 min · 1 practice tasks · quiz
   A net is the solid unfolded, and its total area is the surface area of the solid.
3. Surface area of prisms
   40 min · 1 practice tasks · quiz
   A prism has two identical ends joined by rectangles; add both ends to all the rectangles.
4. Surface area of pyramids
   40 min · 1 practice tasks · quiz
   A pyramid is one base plus triangles meeting at a point; the triangles use the slant height.
5. Area of a sector
   40 min · 1 practice tasks · quiz
   A sector is a fraction of a circle, set by its angle at the centre out of 360 degrees.
6. Area of a segment
   40 min · 1 practice tasks · quiz
   A segment is what is left when the triangle is taken off a sector.
7. Surface area of a cone
   40 min · 1 practice tasks · quiz
   Opened flat, a cone is a sector; its curved surface area is pi r l, and a closed cone adds the base.
8. Surface area of a sphere, and area at work
   40 min · 1 practice tasks · quiz
   A sphere has surface area 4 pi r squared; close the sub-strand by choosing the right method for real surfaces.