Respuesta :
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 [tex]34cm^2[/tex], so we need to know the area of triangle DEF.
From math, let's call [tex]k[/tex] the scaling factor, so we know that for any similar figures, the ratio of the areas of any are in proportion to [tex]k^2[/tex]. In other words, if [tex]A_{1}[/tex] is the area of triangle ABC, and [tex]A_{2}[/tex] is the area of triangle DEF, then we can write the following relationship:
[tex]A_{2}=k^2A_{1} \\ \\ But: \\ \\ A_{1}=34cm^2 \\ \\ \\ Then: \\ \\ \boxed{A_{2}=34k^2}[/tex]
So we have a relationship between the area of triangle ABC and DEF.
The required Area of Triangle DEF is 51cm square.
Given that,
The triangles ABC=DEF
Then, height of ABC= height of DEF
CB = 9cm
FE =13.5cm
Area of ABC= 34cm square
According to the question,
The area of a triangle= [tex]\frac{1}{2}[/tex] × base × height,
Again,
Area of ABC = [tex]\frac{1}{2}[/tex] × base × height= 34cm square
= [tex]\frac{1}{2}[/tex] × 9cm × height= 34cm square
= [tex]\frac{9}{2}[/tex] cm × height= 34cm square
= Height= [tex]\frac{ 34cm square}{\frac{9}{2} }[/tex]
= Height = [tex]\frac{68}{9}[/tex]cm.
The height of the triangle ABC is [tex]\frac{68}{9}[/tex]cm.
Therefore,
Area of DEF = [tex]\frac{1}{2}[/tex]× base × height
= [tex]\frac{1}{2}[/tex] × 13.5cm × ([tex]\frac{68}{9}[/tex])cm
= 51cm square
Therefore, the Area of Triangle DEF is 51cm square.
For more information about Area of Triangle click the link given below.
https://brainly.com/question/11952845
