Answer:
Step-by-step explanation:
Area of shape A = [tex]\frac{1}{2}(\text{Base})(\text{height})[/tex]
= [tex]\frac{1}{2}(4)(5)[/tex]
= 10 square units
Area of shape B = Length × width
= 4×2
= 8 square units
Area of shape C = 5 square units
Area scale factor = [tex](\frac{\text{Area of image}}{\text{Area of original}} )[/tex]
Area scale factor = (Scale factor)²
If scale factor = 2
Area scale factor = 2² = 4
Rule for the dilation,
Area of image = Area scale factor × Area of preimage
Therefore, area of figure A after dilation = 4×10 = 40 square feet
Area of figure B after dilation = 4×8 = 32 square feet
Area of figure C after dilation = 4×5 = 20 square feet
Similarly, we can get areas by different scale factors given in the table.
Scale factor Area of shape A Area of shape B Area of shape C
2 40 32 20
3 90 72 45
10 1000 800 500
[tex]\frac{1}{2}[/tex] 2.5 2 1.25
x 10x² 8x² 5x²
