Question

question 27 points 3 identify the slant height of a regular pentagonal pyramid with the length of an edge of base of 8 centimeters and a lateral area of 250 cm²? 11.5 cm 10.5 cm 13.5 cm 12.5 cm

Explanation:

Step1: Recall the formula for lateral area of a regular pyramid

The lateral area \(L\) of a regular pyramid is given by \(L=\frac{1}{2}Pl\), where \(P\) is the perimeter of the base and \(l\) is the slant height.
For a regular pentagonal pyramid, if the base - edge length \(a = 8\mathrm{cm}\), then the perimeter of the base \(P=5a\). So \(P = 5\times8=40\mathrm{cm}\).

Step2: Solve for the slant height \(l\)

We know that \(L = 250\mathrm{cm}^2\) and \(P = 40\mathrm{cm}\). Substitute into the formula \(L=\frac{1}{2}Pl\).

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Answer:

C. \(12.5\mathrm{cm}\)