To find the surface area , first calculate the height of the triangle.
We can divide it into 2 right triangle and apply the pythagorean theorem:
c^2 = a^2+b^2
Where:
c= hypotenuse = 14
a = 14/2 = 7
b= height
Replacing:
14^2 = 7^2 + b^2
Solve for b
196= 49+b^2
196-49=b^2
147 = b^2
√147= b
b= 12.1 ft
Now, calculate the area of each rectangular face and each triangular face:
Area of a triangle = 1/2 x base x height = 1/2 x 14 x 12.1 = 84.8 ft2
Area of a rectangle = length x width = 14 x 10 = 140 ft2
Since it has 2 triangular faces and 3 rectangular faces
SA = 2 (84.7) + 3 (140) = 169.4+420= 589.7 ft2