Question

Find the surface area of the figure below.

Answer 1

We have two equilateral triangles and three rectangles.

The formula of an area of an equilateral triangle:

$A_{\triangle}=\dfrac{a^2\sqrt3}{4}$

a - length of side

We have a = 14 ft. Substitute:

$A_{\triangle}=\dfrac{14^2\sqrt3}{4}=\dfrac{196\sqrt3}{4}=49\sqrt3\ in^2$

The formula of an area of a rectangle:

$A_{\boxed{\ }}=lw$

l - length

w - width

We have l = 10ft and w = 14 ft. Substitute:

$A_{\boxed{\ }}=(10)(14)=140\ ft^2$

The Surface Area of the figure:

$S.A.=3A_{\boxed{\ }}+2A_{\triangle}\\\\S.A.=3\cdot140+2\cdot49\sqrt3=(420+98\sqrt3)\ ft^2$