Question

The figures are similar. Find the area. The area of △ △ A B C is 15 square cm. The height of △ △ A B C is 5 cm and the height of △ △ D E F is 13 cm. Find the area of △ △ D E F . Round to the nearest square cm if necessary.

Answer 1

The area of triangle DEF is
`282\ cm^(2)`

Explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

To find the scale factor, divide the height of triangle DEF by the height of triangle ABC

Let

z ------> the scale factor

`z=(13)/(5)`

step 2

Find the area of triangle DEF

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z -----> the scale factor

x ----> the area of triangle DEF

y -----> the area of triangle ABC

`z^(2)=(x)/(y)`

we have

`z=(13)/(5)`

`y=15\ cm^(2)`

substitute and solve for x

`((13)/(5))^(2)=(x)/(15)`

`x=((169)/(25))(15)`

`x=282\ cm^(2)`