Answer:

510

Step-by-step EXPLANATION:

Here,

   Total area is 2160 inch^2.

Given,

     Area covered by TRIANGLES is 432 inch^2 ;

     Area covered by squares is 180 inch^2

Lorea wants to the cover the remaining area with the parallelograms of base 2 inch and height 1.5 inch.

     We know, area of parallelogram is given by the PRODUCT of its base and height.

  So, area of each parallelogram should be 2 x 1.5 inch^2 = 3 inch^2

Let there are N parallelograms, so total area covered by the parallelograms is 3 inch^2 + 3 inch^2 + 3 inch^2 + ...upto n times, which can be written as 3n inch^2.

  Total area = area covered by triangles + area covered by squares + area covered by parallelogram.

    2160 = 432 + 180 + 3n

  ⇒ 2160 - 432 - 180 = 3n

  ⇒ 1548 = 3n

  ⇒ 510 = n   { divide by 3 }

Hence the correct option is 510.

Looking for a short answer ?  let there are n parall.

  total area = ar. of triangle + ar. of squares + ( 1.5 x 2 x n )

  2160 - 432 - 180 = 3n

  1548 = 3n

  510 = n