We have two equilateral triangles and three rectangles.
The formula of an area of an equilateral triangle:
[tex]A_{\triangle}=\dfrac{a^2\sqrt3}{4}[/tex]
a - length of side
We have a = 14 ft. Substitute:
[tex]A_{\triangle}=\dfrac{14^2\sqrt3}{4}=\dfrac{196\sqrt3}{4}=49\sqrt3\ in^2[/tex]
The formula of an area of a rectangle:
[tex]A_{\boxed{\ }}=lw[/tex]
l - length
w - width
We have l = 10ft and w = 14 ft. Substitute:
[tex]A_{\boxed{\ }}=(10)(14)=140\ ft^2[/tex]
The Surface Area of the figure:
[tex]S.A.=3A_{\boxed{\ }}+2A_{\triangle}\\\\S.A.=3\cdot140+2\cdot49\sqrt3=(420+98\sqrt3)\ ft^2[/tex]
