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Vesna [10]
3 years ago
7

8. The trapezoids are similar. The area of the smaller trapezoid is 131 m2. Find the area of the larger trapezoid to the nearest

whole number.

Mathematics
1 answer:
kolbaska11 [484]3 years ago
5 0

Answer:

3,726\ m^{2}

Step-by-step explanation:

step 1

Find the scale factor

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----> corresponding side of the larger trapezoid

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

z=\frac{x}{y}

we have

x=64\ m

y=12\ m

substitute

z=\frac{64}{12}

step 2

Find the area of the larger trapezoid

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----> area of the larger trapezoid

y----> area of the smaller trapezoid

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

we have

z=\frac{64}{12}

y=131\ m^{2}

substitute

(\frac{64}{12})^{2}=\frac{x}{131}

x=(\frac{4,096}{144})(131)

x=3,726\ m^{2}

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