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

Answer:

$\boxed{\text{144.33 m}^{2}}$

Step-by-step 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.

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