Question

triangles ABC and DEF are mathematically similar. The area of triangles ABC is 34cm^2. Calculate the area of triangle DEF.

Answer 1

Explanation:

First of all, what are similar shapes? Well, two shapes are similar if you can turn one into the other by moving, rotating, flipping, or scaling. That means you can make one shape bigger or smaller. In this case, we know that triangles ABC and DEF are mathematically similar. The area of triangles ABC is $34cm^2$, so we need to know the area of triangle DEF.

From math, let's call $k$ the scaling factor, so we know that for any similar figures, the ratio of the areas of any are in proportion to $k^2$. In other words, if $A_{1}$ is the area of triangle ABC, and $A_{2}$ is the area of triangle DEF, then we can write the following relationship:

$A_{2}=k^2A_{1} \\ \\ But: \\ \\ A_{1}=34cm^2 \\ \\ \\ Then: \\ \\ \boxed{A_{2}=34k^2}$

So we have a relationship between the area of triangle ABC and DEF.