A pyramid of canvas
A festival tent has a square base and four triangular walls.
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- A square base, apex above the middle.
- The height runs straight down to the centre.
- The slant runs to the middle of a base edge.
- The slant is the longer side, not the height.
The rule
A pyramid stands on a flat base. Its triangular walls meet at the apex.
Take a square pyramid. Its apex is above the middle of the base. Its height runs straight down from the apex to the centre. Each wall is a triangle. The wall's height joins the apex to a base edge's middle. That is the slant height.
volume of a pyramid = ⅓ × base area × height
Take a square base of side 6 m, with height 4 m. The base area is 6 × 6 = 36 m². The pyramid holds ⅓ × 36 × 4 = 48 m³.
A right triangle sits inside the pyramid. Its sides: height h, half the base side, slant l. The longest side squared equals the other two sides squared, added.
l² = (base ÷ 2)² + h²
Half the base side is 6 ÷ 2 = 3 m. Here 3² = 9 and 4² = 16.
l = √(9 + 16) = √25 = 5 m.
The canvas covers the four walls only. One wall is ½ × 6 × 5 = 15 m². Four walls need 4 × 15 = 60 m² of canvas.
| Wall built on | One wall | Four walls |
|---|---|---|
| The slant, 5 m | 15 m² | 60 m² |
| The height, 4 m | 12 m² | 48 m² |
Buy 48 m² by the height. Then 12 m² of the tent stays bare.