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hoa [83]
2 years ago
13

are any two regular polygons similar. The area of the smaller figure is about 390 cm^2. choose the best estimate of the area of

the larger figure

Mathematics
1 answer:
galben [10]2 years ago
4 0

Answer:

The best estimate of the area of the larger figure is 693\ cm^{2}

Step-by-step explanation:

step 1

<em>Find the scale factor</em>

we know that

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

Let

z----> the scale factor

x-----> the corresponding side of the larger figure

y-----> the corresponding side of the smaller figure

so

z=\frac{x}{y}

we have

x=12\ cm

y=9\ cm

substitute

z=\frac{12}{9}=\frac{4}{3} -----> the scale factor

step 2

<em>Find the area of the larger figure</em>

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 figure

y-----> the area of the smaller figure

so

z^{2}=\frac{x}{y}

we have

z=\frac{4}{3}

y=390\ cm^{2}

substitute and solve for x

(\frac{4}{3})^{2}=\frac{x}{390}

(\frac{16}{9})=\frac{x}{390}

x=390*16/9=693.33\ cm^{2}

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