Question

The surface area of a pyramid is 327 square meters. what is the surface area of a similar pyramid that is smaller by a scale factor of 2 − 3 ? round to the nearest hundredth if necessary

Answer 1

`\boxed{\text{144.33 m}^(2)}`

Explanation:

The scale factor (C) is the ratio of corresponding parts of the two pyramids.

The ratio of the areas is the square of the scale factor.

`(A_(1))/( A_(2)) = C^(2)\\\\\frac{\text{327 m}^(2)}{A_(2)} = \left ((1)/((2)/(3))\right)^(2)\\\\ \frac{\text{327 m}^(2)}{A_(2)}= (9)/(4)\\\\\text{1308 m}^(2)= 9A_(2)\\\\A_(2) = \text{145.33 m}^(2)\\\text{The surface area of the smaller pyramid is \boxed{\text{145.33 m}^(2)}}`