Answer:
[tex]\large\boxed{C.\ (25+25\sqrt3)\ in^2}[/tex]
Step-by-step explanation:
We have the square and four equilateral triangles.
The formula of an area of a squre:
[tex]A_S=a^2[/tex]
a - length of side
The formula of an area of an equilateral triangle:
[tex]A_T=\dfrac{a^2\sqrt3}{4}[/tex]
a - length of side
Clculate the areas:
SQURE:
[tex]A_S=x^2\ in^2[/tex]
TRIANGLE:
[tex]A_T=\dfrac{x^2\sqrt3}{4}\ in^2[/tex]
The SURFACE AREA of a square pyramid:
[tex]S.A.=A_S+4A_T\\\\S.A.=x^2+4\cdot\dfrac{x^2\sqrt3}{4}=x^2+x^2\sqrt3[/tex]
Put x = 5:
[tex]S.A.=5^2+5^2\sqrt3=(25+25\sqrt3)\ in^2[/tex]
