Question

3. Carlos cuts blue parallelograms and larger red parallelograms to use in his decoupage. He realizes the parallelograms are similar. What is the Round to the nearest tenth area of the larger, red parallelogram? Round to the nearest tenth

Answer 1

The area of the larger parallelogram is
`180\ 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 the scale factor

Let

z------> the scale factor

`z=(24)/(16)=1.5`

step 2

Find the area of the larger parallelogram

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 the larger parallelogram

y-------> the area of the smaller parallelogram

so

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

we have

`z=1.5`

`y=80\ cm^(2)`

substitute the values

`1.5^(2)=(x)/(80)`

`x=80*(1.5^(2))=180\ cm^(2)`