Answer:
[tex]\bigtriangleup= 19.84\ in^2[/tex]
Step-by-step explanation:
We calculate the initial area before the dimension modifications.
-The surface area(given the slant height) is calculated as:
[tex]A=Base \ Area +Triangle:s \ Area\\\\=s^2+4(0.5sh)\\\\s=base \ side, h=\ slant \ height\\\\\therefore A=4^2+4(0.5\times 8\times 4)\\\\=80\ cm^2[/tex]
-If the slant height is tripled, the new height will be 3*8=24, and the base lengths remain unchanged:
[tex]A_n=Base \ Area +Triangle:s \ Area\\\\=s^2+4(0.5sh)\\\\s=base \ side, h=\ slant \ height\\\\\therefore A_n=4^2+4(0.5\times 24\times 4)\\\\=208\ cm^2[/tex]
-The change in area is calculated as (1 sq cm=0.155 sq in):
[tex]\bigtriangleup=A_n-A\\\\=128\ cm^2\\\\=>1 \ cm^2=0.155\ in^2\\\\\therefore 128\ cm^2=0.155\ in^2\times 128\\\\=19.84\ in^2[/tex]
