3. Calculate to one decimal place the number of cubic meters of air under a tent in the shape of a pyramid, which is composed of four tent panels in the shape of isosceles triangles with a base length of $24 \mathrm{dm}$ and a leg length of $21 \mathrm{dm}$. The base of this pyramid is a square. Draw a sketch.
3. Since the base of the pyramid is a square, its sides are 24 dm long. (If they were 21 dm long, we would not be able to form the pyramid from the triangles.) We calculate the length of the diagonal of the base of the pyramid; \( |A C| = d = a \sqrt{2} = 24 \sqrt{2} \, \text{dm} \). Using the right triangle \( A F E \) and the Pythagorean theorem, we calculate the height of the pyramid with the equation; \( v^2 = s^2 - \left( \frac{d}{2} \right)^2 \). We substitute the values, take the square root, and calculate the approximate value \( v = 1.237 \, \text{m} \). We substitute the values into the formula for the volume of a regular quadrilateral pyramid \( V = \frac{a^2 v}{3} \). We calculate \( V = 2.4 \, \text{m}^3 \).

Narisana skica 1 točka

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