find the slant height of the square pyramid

Question

12
10

Answer 1

To find the slant height of a square pyramid, we need to know the height of the pyramid and the length of one side of the base. In your case, you have provided the values 12 and 10, which I will assume refer to the height (h) and half the base length (b/2) respectively.

1. Identify the base length (b): Since you provided half the base length (10), the full base side length would be: $$b=2\times 10=20$$

2. Determine the height of the pyramid (h): The height of the pyramid is given as 12.

3. Calculate the slant height (l): The slant height of a square pyramid can be found using the Pythagorean theorem. The slant height forms a right triangle with half of the base and the height of the pyramid: $$l=\sqrt{h^2+{\left(\frac{b}{2}\right)}^2}$$ Here, $\frac{b}{2}$ is the distance from the center of the base to the edge of the base, which we know is 10.

   Plugging the values into the equation: $$l=\sqrt{{12}^2+{10}^2}$$ $$l=\sqrt{144+100}$$ $$l=\sqrt{244}$$ $$l\approx 15.62$$

Thus, the slant height of the square pyramid is approximately 15.62 units.