Question

Polygon C has an area of 40 square units. Kennan drew a scaled version of Polygon C using a scale factor of 1/2 and labeled it Polygon D. What is the area of Polygon D?

a) 10 square units
b) 20 square units
c) 40 square units
d) 80 square units

Answer 1

The area of Polygon D is 10 square units, achieved by squaring the scale factor of 1/2 and multiplying it by the area of Polygon C which is 40 square units.

Step-by-step explanation:

When scaling a polygon, the area scales by the square of the scale factor. Since Polygon C has an area of 40 square units and Polygon D is drawn using a scale factor of 1/2, we can determine the area of Polygon D by squaring the scale factor and then multiplying it by the area of Polygon C.

Calculating the area of Polygon D:

• Scale factor = 1/2
• Square of the scale factor = (1/2)2 = 1/4
• Area of Polygon D = 40 square units * (1/4)
• Area of Polygon D = 10 square units

Therefore, the correct answer is a) 10 square units.