Answer:
The area of the smaller triangle is 80m²
Step-by-step explanation:
Find the scale factor to get the dimensions of the smaller triangle from the larger triangle using the given information:
[tex]\frac{\text{Large Triangle Length}}{\text{Small Triangle Length}}=\frac{12}{8}=\frac{3}{2}[/tex]
When scaling the area of similar shapes, we will square the scale factor for the lengths. We do this because area is a 2-dimensional measurement.
[tex](\frac{3}{2})^2=\frac{9}{4}[/tex]
Let x represent the area of the smaller triangle. So, we have:
[tex]\frac{9}{4}=\frac{180}{x}[/tex]
Cross multiply:
[tex]9x=4(180)[/tex]
[tex]9x=270[/tex]
Divide by 9:
[tex]x=\frac{720}{9}[/tex]
[tex]x=80[/tex]
Therefore, the area of the smaller triangle is [tex]80m^2[/tex].
