Question

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.

Answer 1

`3,726\ m^(2)`

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=(x)/(y)`

we have

`x=64\ m`

`y=12\ m`

substitute

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

we have

`z=(64)/(12)`

`y=131\ m^(2)`

substitute

`((64)/(12))^(2)=(x)/(131)`

`x=((4,096)/(144))(131)`

`x=3,726\ m^(2)`