Answer: The approximate surface area of the larger pyramid is 159.31 ft².
Step-by-step explanation:
A pyramid is a solid,
And, When two solids are similar then the ratio of their surface area is the square of the scale factor of similarity.
Here, the scale factor of similarity
[tex]=\frac{\text{Height of larger pyramid}}{\text{Height of smaller pyramid}}[/tex]
[tex]=\frac{15}{6}[/tex]
Thus, by the above property,
[tex]\frac{\text{ The surface area of larger pyramid}}{\text{The surface area of the smaller pyramid}}=(\frac{15}{6})^2[/tex]
It is given that, the smaller pyramid has a surface area of 25.49 ft²,
[tex]\implies \frac{\text{ The surface area of larger pyramid}}{25.49}=\frac{225}{36}[/tex]
[tex]\text{ The surface area of larger pyramid} = \frac{25.49\times 225}{36}[/tex]
[tex]=\frac{5735.25}{36}[/tex]
[tex]=159.3125\approx 159.31\text{ square ft}[/tex]
The surface area of the larger pyramid is 159.31 square feet.
Given
The two hexagonal pyramids are similar.
If the smaller pyramid has a surface area of 25.49 ft2.
A pyramid that has sides or faces in the shape of isosceles triangles that form the hexagonal pyramid at the top of the pyramid.
When two solids are similar then the ratio of their surface area is the square of the scale factor of similarity.
The scale factor of similarity is;
[tex]\rm Scale \ factor = \dfrac{Height \ of \ large \ pyramid}{Height \ of \ small \ pyramid}\\\\ Scale \ factor =\dfrac{15}{6}[/tex]
The surface area of the pyramid is directly proportional to the square of the height i
[tex]\rm Surface \ area = 25.49 \times \dfrac{15^2}{6^2}\\\\ Surface \ area = 25.49 \times \dfrac{225}{36}\\\\ Surface \ area= \dfrac{5735.25}{36}\\\\Surface \ area = 159.31[/tex]
Hence, the surface area of the larger pyramid is 159.31 square feet.
To know more about Pyramid click the link given below.
https://brainly.com/question/243773
