Final answer:
To find the height of a pyramid with a known lateral area and base edge length, the area of one of the side triangles is first identified, then the Pythagorean theorem is applied with the slant height to find the height of the pyramid.
Step-by-step explanation:
The student has asked about finding the height of a pyramid with a given lateral area and base edge length. As the base of the pyramid is square with edges each 48 inches long, we can determine the slant height of the pyramid's side triangle using the area of the four congruent triangles that make up the lateral area.
First, we calculate the area of one triangle by dividing the total lateral area by 4 (since there are four triangles): 2400 in² / 4 = 600 in².
Next, we use the formula for the area of a triangle, 1/2 × base × height, which gives us 1/2 × 48 in × slant height = 600 in², leading to a slant height of 25 in.
We can now use the Pythagorean theorem, considering the slant height as the hypotenuse of a right-angled triangle where the other sides are the half of the base edge and the pyramid's height. Assuming the height is 'h' and using the formula h² + (48/2)² = 25², we can solve for 'h' to find the height.