Question

1. the pyramid pictured below has a total surface area of 336 centimeters squared. find the missing lateral height, x.

Explanation:

Step1: Calculate base area

$A_{base} = 12 \times 12 = 144$ cm²

Step2: Find total lateral surface area

$A_{lateral, total} = 336 - 144 = 192$ cm²

Step3: Area of one triangular face

$A_{triangle} = \frac{192}{4} = 48$ cm²

Step4: Solve for lateral height x

Use triangle area formula: $A_{triangle} = \frac{1}{2} \times base \times x$
$48 = \frac{1}{2} \times 12 \times x$
$48 = 6x$
$x = \frac{48}{6} = 8$

Answer:

8 cm