the square pyramid below has a height of 12 centimeters and a slant height of 20 centimeters. the square…

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

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

Answer

Explanation:

Step1: Recall lateral - area formula

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

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

Step3: Calculate the lateral area

We know that the slant height (l = 20) cm. Using the formula (L=\frac{1}{2}Pl), we substitute (P = 128) cm and (l = 20) cm. Then (L=\frac{1}{2}\times128\times20). [ \begin{align*} L&=\frac{128\times20}{2}\ &=1280\text{ cm}^2 \end{align*} ]

Answer:

1280 cm²