Answer:
[tex]85in^2[/tex]
Step-by-step explanation:
to find the surface area we need to find the followng areas:
- area of a triangle and multiply it by 4 (because there are 4 triangles)
And once we have those areas, we add them to find the surface area.
Area of the square:
the formula to find the area of a square is:
[tex]a_{square}=l^2[/tex]
where [tex]l[/tex] is the length of the side: [tex]l=5in[/tex]
thus the area of the square is:
[tex]a_{square}=(5in)^2\\a_{square}=25in^2[/tex]
Area of the triangles:
the are of 1 triangle is given by
[tex]a_{triangle}=\frac{b*h}{2}[/tex]
where [tex]b[/tex] is the base of the triangle: [tex]b=5in[/tex] (the base of the triangle is the side of the square)
and [tex]h[/tex] is the height of the triangle: [tex]h=6in[/tex]
thus, the area of 1 triangle is:
[tex]a_{triangle}=\frac{(5in)*(6in)}{2}\\ a_{triangle}=\frac{30in^2}{2}\\ a_{triangle}=15in^2[/tex]
the area of the 4 triangles is (we multiply by 4):
[tex]a_{4-triangles}=4(15in^2)\\a_{4-triangles}=60in^2[/tex]
finally we add the area of the square and the area of the 4 triangles to find the total surface area:
[tex]Surface=25in^2+60in^2\\Surface=85in^2[/tex]
