Given the following shapes: a rectangle with width 6 and height 4, a square with side 9, a right_triangle with base 9 and height 6, a right_triangle with base 7 and height 3, a right_triangle with base 4 and height 8, a trapezoid with bases 4 and 6 and height 3. What is the total area of all shapes? Please round the result to the nearest integer.
<think>Rectangle with width 6 and height 4: Area = 6 x 4 = 24
Square with side 9: Area = 9^2 = 81
Right triangle with base 9 and height 6: Area = 0.5 x 9 x 6 = 27.0
Right triangle with base 7 and height 3: Area = 0.5 x 7 x 3 = 10.5
Right triangle with base 4 and height 8: Area = 0.5 x 4 x 8 = 16.0
Trapezoid with bases 4, 6 and height 3: Area = 0.5 x (4 + 6) x 3 = 15.0</think>

<answer>174</answer>