Find the area of the figure. Please help me

Suppose that the altitude drawn intersects the base of PQRS at point 'T'.  

With our triangle RTQ, we can clearly see that the angle of 'T' is 90° and angle R is 30°. All triangular angles equal to 180°, so angle Q= 180° - 90° - 30° = 60°. This concludes in triangle RTQ is a 30°-60°-90° right-amg;e triangle!

The sides of the 30°-60°-90° triangle are in ratio 1:√3:2 (the side opposite to the angle 30°):(side opposite to the 60° angle):(side opposite to the 90° angle)). Our hypotenuse, the side opposite to the 90° angle, values length of 24. The altitude of the triangle, the side opposite to the 30° angle, therefore has a length of 24 divided by 2 = 12; so the base of our triangle, the side opposite to the 60° angle, has a length of 12√3.

So we calculate that...

(the area of the left trapezoid) + (area single triangle*)

= (1/2)x(6 + 18)x(12) + (1/2)x(12√3)x(12)

= 144 + 72√3.

Step-by-step explanation:

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step-by-step explanation: