Answer
Total area of the shape = 5905.9 cm$^{2}$
Work Step by Step
To find the are of the shape we simply need to break the shape into two separate trapezoids, find the area of each trapezoid, and add the results together.
Area of a Trapezoid = $A$ = $\frac{1}{2}$$h$($b$ + $B$)
Therefore:
$A$$_{top}$ = $\frac{1}{2}$(46.2 cm)(61.7 cm + 87.3 cm)
$A$$_{top}$ = $\frac{1}{2}$(46.2 cm)(149 cm)
$A$$_{top}$ = (23.1 cm)(149 cm)
$A$$_{top}$ = 3441.9 cm$^{2}$
$A$$_{bottom}$ = $\frac{1}{2}$(46.2 cm)(61.7 cm + 92.3 cm)
$A$$_{bottom}$ = $\frac{1}{2}$(32 cm)(154 cm)
$A$$_{bottom}$ = (16 cm)(154 cm)
$A$$_{bottom}$ = 2464 cm$^{2}$
Total Area = $A$$_{total}$ = $A$$_{top}$ + $A$$_{bottom}$
$A$$_{total}$ = 3441.9 cm$^{2}$ + 2464 cm$^{2}$
$A$$_{total}$ = 5905.9 cm$^{2}$
