The scale factor is 5/4. Find the area of the pre-image if the area of the image is 150 in2.Show your work.

Ap = 5/4 * 150in^2 = 187.5 in^2.

To find the area of the pre-image, we can use the scale factor. The formula to find the relationship between the areas of the pre-image and the image is:

Area of pre-image / Area of image = (Scale factor)^2

In this case, the scale factor is 5/4, so we can substitute it into the formula:

Area of pre-image / 150 in^2 = (5/4)^2

To solve for the area of the pre-image, we can cross-multiply:

Area of pre-image = 150 in^2 * (5/4)^2

Now we can calculate this expression:

Area of pre-image = 150 in^2 * (5/4)^2
= 150 in^2 * (25/16)
= (150 * 25) / 16 in^2
= 3750 / 16 in^2

Therefore, the area of the pre-image is 3750/16 square inches.

Note: In case the original shape was a two-dimensional figure, the new shape and the pre-image would be similar. In this case, the scale factor squared is used in the formula because we are dealing with areas, and the scale factor applies to both dimensions (length and width).