Question

Polygon Q is a scaled copy of polygon P using a scale factor of 1/2. Polygon Q's area is what fraction of polygon P's area?

A. 1/4
B. 1/2
C. 2/3
D. 1

Answer 1

Polygon Q's area, as a scaled copy of Polygon P with a scale factor of 1/2, will be 1/4 the area of Polygon P, since area is proportional to the square of the dimensions.

Step-by-step explanation:

When Polygon Q is a scaled copy of Polygon P using a scale factor of 1/2, this means that each dimension (length, width, etc.) of Polygon Q is 1/2 the corresponding dimension of Polygon P. Since the area of a figure is proportional to the square of its dimensions, the area of Polygon Q will be the square of the scale factor (1/2) times the area of Polygon P, which is (1/2)² or 1/4. Therefore, Polygon Q's area is 1/4 the area of Polygon P.

Here's an example to illustrate this concept. Imagine a square as Polygon P with side length s. Its area is s². If we now create a scaled copy, Polygon Q, with a scale factor of 1/2, the new side length will be 1/2s, and its area will be (1/2s)² = 1/4s². So, the area of Polygon Q is 1/4 that of Polygon P.