Final answer:
The area of Patty's tapestry, which is a parallelogram, is 12 square feet, obtained by multiplying the base and height (3 feet × 4 feet). Similar to comparing a scaled square, where the area increases by the square of the scale factor.
Step-by-step explanation:
To calculate the area of the tapestry, which is a parallelogram, you multiply the base by the height. Given that the tapestry has a base of 3 feet and a height of 4 feet, the area is calculated as follows:
Area = base × height
Area = 3 feet × 4 feet
Area = 12 square feet
This is similar to the example where Marta has a square with a side length of 4 inches, and a second square with dimensions twice the first square. The area of the larger square is 4 times larger than the area of the smaller square because if the side length doubles, the area, being side length squared, increases by a factor of four (22).
For scale drawings, the scale factor is crucial. If a drawing has a scale factor of 1/24, you would need to multiply the lengths in the drawing by 24 to find the actual size, and then calculate the area.
Regarding tapestries, they can be ornate pieces of fabric featuring designs such as parallelograms, and historically, they have served both as artistic and practical purposes.