Geometry and Measurement — Surface area of pyramids and cones

About this lesson

This unit teaches students how to calculate the lateral area and total surface area of regular pyramids and right circular cones. It begins by reviewing properties of these solids and their nets, then presents formulas: for a regular pyramid, lateral area equals half the perimeter of the base times the slant height, and total area adds the base area. For a right cone, lateral area equals π times the radius times the slant height, and total area adds the base area (πr²). Worked examples include finding areas from nets, given dimensions, and a real-world problem about painting a buoy shaped as two cones with a common base. Exercises ask students to compute areas for various pyramids and cones, and to find a cone's radius given its total area and slant height. By the end, students should be able to apply these formulas to solve mathematical and practical problems involving surface areas of pyramids and cones.