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In the diagram, △ABC∼△DEF. The area of △ABC is 180 square centimeters. Find the area of △DEF.

pls pls pls help me answer

In the diagram ABCDEF The area of ABC is 180 square centimeters Find the area of DEF pls pls pls help me answer class=

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Answer:

20

Step-by-step explanation:

The first step is to find out the similarity reason of the sides of the triangle, so we just divide the big side by the small side (12/4=3).

Now, for the similarity reason of the areas, we just square that number (3^2=9).

Then we just divide the area of the big triangle by 9, which is 180/9= 20.

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. The area of the △DEF is 20cm².

What are Similar Figures?

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".

Given △ABC∼△DEF, therefore, the sides will be in a particular ratio,

Ratio = AB/DE = 12/4 = 3

Also, the area of △ABC is 180 square centimeters. since the area is a two-dimensional quantity it will be the product of two sides, therefore, the ratio will also be multiplied twice. Thus, the area of △DEF will be 1/9 of the area of △ABC. Hence, the area of △DEF is,

△DEF = △ABC/9

△DEF = 180cm²/9 = 20cm²

Hence, the area of the △DEF is 20cm².

Learn more about Similar Figures:

https://brainly.com/question/11315705

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