Given the following shapes: a square with side 6, a trapezoid with bases 2 and 9 and height 6, a rectangle with width 6 and height 4, a square with side 7, a trapezoid with bases 6 and 1 and height 7, a trapezoid with bases 5 and 2 and height 2. What is the total area of all shapes? Please round the result to the nearest integer.
<think>Square with side 6: Area = 6^2 = 36
Trapezoid with bases 2, 9 and height 6: Area = 0.5 x (2 + 9) x 6 = 33.0
Rectangle with width 6 and height 4: Area = 6 x 4 = 24
Square with side 7: Area = 7^2 = 49
Trapezoid with bases 6, 1 and height 7: Area = 0.5 x (6 + 1) x 7 = 24.5
Trapezoid with bases 5, 2 and height 2: Area = 0.5 x (5 + 2) x 2 = 7.0</think>

<answer>174</answer>