Question

"∆ABC~∆DEF. The area of ∆ABC is given. Find the area of ∆DEF. Do not lable the final answer."

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

∆ABC~∆DEF

triangle 1:

AC = 10

area = 65 in²

triangle 2:

DF = 20

area = ?

Step 02:

We must apply the rules of similar triangles to find the solution. .

`\frac{triangle\text{ 1 AC}}{\text{triangle 2 DF }}=\frac{triangle\text{ 1 area}}{\text{triangle 2 area}}`
`(10)/(20)=\frac{65in^2}{triangle\text{ 2 area}}`

triangle 2 area * 10 = 65 in² * 20

triangle 2 area = (65 in² * 20 ) / 10

= 130 in²

The answer is:

The area of the big triangle is 130 in² .