Answer:
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.
Explanation:
HOPE THIS HELPS!!