Answer:
298.13 square units
Step-by-step explanation:
To find the area of triangle ABC after it undergoes a dilation by a scale factor of 2.5, dilate the lengths of its base and height by 2.5, then calculate the area using the dilated lengths.
[tex]\textsf{Dilated height:}\quad a_1 = 10.6 \times 2.5 = 26.5[/tex]
[tex]\textsf{Dilated base:}\quad b_1 = 9.0 \times 2.5 = 22.5[/tex]
Therefore:
[tex]\begin{aligned}\textsf{Area of $\triangle A'B'C'$}&=\dfrac{1}{2} \times b_1 \times a_1\\\\&=\dfrac{1}{2} \times 22.5 \times 26.5\\\\&=11.25 \times 26.5\\\\&=298.125\\\\&=298.13 \; \sf square\;units\;(nearest\;hundredth)\end{aligned}[/tex]
So, the area of triangle ABC after it undergoes a dilation by a scale factor of 2.5 is:
[tex]\Large\boxed{\boxed{298.13\; \sf square\;units}}[/tex]
