Gr 6–8 · 45 min
Surface area of a pyramid
Coming soon. We're checking this lesson against the app, step by step, so it works when you run it with a class. You can read the plan now. The lesson pack, teaching mode and assigning open once it's checked.
A square pyramid's net is a square and four triangles; the slant height, not the height, gives their area.
Ontario Gr 6–8 · Spatial Sense E2 · Common Core 6.G.A.4, 8.G.B.7
Learning goals
- Find a pyramid's surface area from its net
- Tell the slant height of a face from the height of the pyramid
- Use the Pythagorean theorem to find the slant height (grade 8)
Plan
- 1
Unfold5 minStudents
Look at the net: one square base and four matching triangles. Which of these lengths can you see on the net?
- 2
Measure10 minStudents
Measure the height of one triangle, from the middle of its base to its tip. That's the slant height: 5 cm.
- 3
Calculate10 minStudents
Each triangle is ½ × 6 × 5 = 15 cm². Four of them plus the 36 cm² base: 96 cm².
- 4
Why 5?10 minStudents
Build the pyramid. Inside, the height (4 cm), half the base (3 cm) and the slant height make a right triangle: 3² + 4² = 5².
- 5
Try another10 minYou lead
On the board, change the pyramid's height in FoldNets. Students predict the new slant height and surface area, then turn on Heights to see the slant height on the net.
To talk about
- Why isn't the pyramid's height (4 cm) the height of its triangles?
- What happens to the surface area as the pyramid gets taller but keeps its base?