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?

Answer 1

Solution:

Pre-image = Polygon P

Image = Polygon Q

When we Dilate Polygon P→(Pre- image) by a scalar factor of $\frac{1}{2}$ we get Polygon Q.

→Size of Polygon P > Size of Polygon Q

As The shape and size of  image that is Polygon Q changes , but the interior angles of polygon Q and polygon P will be same after dilation.

So, the two polygons will be Similar.

As it is also given that Polygon Q is a scaled copy of Polygon P using a scale factor of 1/2 .

⇒$\frac{\text{Area of Polygon P}}{\text{Area of Polygon Q}}=\frac{2}{1}$

⇒Area of Polygon Q = $\frac{1}{2}$ × Area of Polygon P

Answer 2

Answer:

1/4

Step-by-step explanation:

This question is testing the relationship between the linear scale factor and the area scale factor.

In this case we have been given the linear scale factor.

Given the linear scale factor, the area scale factor is given by the square of the linear scale factor.

LSF = Linear scale factor = 1/2

The area scale factor is the square of 1/2 which is :

= 1/2 × 1/2 = 1/4

The area of polygon Q is thus 1/4 times the area of polygon P.