Question

1. find the slant height of the pyramid. use the image to show your work. round to the nearest hundredth.

Explanation:

Step1: Apply Pythagorean theorem

Let the base - related length be half of the side length of the base square. Since the side length of the base square is 7 mm, the base - related length \(a=\frac{7}{2}=3.5\) mm, and the vertical height of the right - triangle formed inside the pyramid is 6 mm. The slant height \(l\) is the hypotenuse of a right - triangle. According to the Pythagorean theorem \(l=\sqrt{6^{2}+3.5^{2}}\).

Step2: Calculate the value

First, calculate \(6^{2}=36\) and \(3.5^{2}=12.25\). Then \(6^{2}+3.5^{2}=36 + 12.25=48.25\). So \(l=\sqrt{48.25}\approx6.95\) mm.

Answer:

6.95 mm