Question

a triangle has a base of 25 feet and a height of 12 feet. if a dilation with a scale factor of k = 3 is applied, what is the new area? 1,350 ft² 675 ft² 450 ft² 150 ft²

Explanation:

Step1: Find the original area formula

The area formula of a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Step2: Calculate the original area

Given $b = 25$ feet and $h=12$ feet, so the original area $A_{1}=\frac{1}{2}\times25\times12=\frac{1}{2}\times300 = 150$ square - feet.

Step3: Determine the relationship between original and new - area after dilation

When a dilation with a scale factor $k$ is applied to a two - dimensional figure, the ratio of the new area $A_{2}$ to the original area $A_{1}$ is $k^{2}$. That is $A_{2}=k^{2}A_{1}$.

Step4: Calculate the new area

Since $k = 3$ and $A_{1}=150$ square - feet, then $A_{2}=3^{2}\times150=9\times150 = 1350$ square - feet.

Answer:

$1,350\ ft^{2}$