Question

the square pyramid below has a height of 12 centimeters and a slant height of 20 centimeters. the square base of the pyramid has side lengths of 32 centimeters. what is the lateral area of the pyramid? 384 cm² 640 cm² 768 cm² 1280 cm²

Explanation:

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

The lateral area \(L\) of a square pyramid is given by \(L = \frac{1}{2}Pl\), where \(P\) is the perimeter of the base and \(l\) is the slant height.

Step2: Calculate the perimeter of the base

Since the base is a square with side length \(s = 32\) cm, the perimeter \(P=4s\). So, \(P = 4\times32=128\) cm.

Step3: Substitute values into the lateral - area formula

We know that \(P = 128\) cm and \(l = 20\) cm. Then \(L=\frac{1}{2}\times128\times20\).
First, \(\frac{1}{2}\times128 = 64\). Then \(64\times20=1280\) \(cm^{2}\).

Answer:

\(1280\ cm^{2}\) (the fourth option)