Question

The figures below are similar. the area of the larger trapezoid is 121m^2. Find the area of the smaller trapezoid to the nearest square meter. Please help!

Answer 1

Answer:

54 square meters

Step-by-step explanation:

Similar figures have corresponding lengths as equal ratios.

Smaller trapezoid's base is given 12 and larger trapezoids base is given 18, so the scale factor is $12k=18\\k=\frac{18}{12}\\k=1.5$

this means the lengths of larger is 1.5 times lengths of smaller.

In terms of area, the scale factor is squared. Hence the scale factor for area is  $k^2=(1.5)^2=2.25$

this means the area of larger is 2.25 times the area of smaller.

Now, Let area of smaller trapezoid be x so we can say:  $x(2.25)=121\\x=\frac{121}{2.25}\\x=53.78$

to nearest square meter, x = 54 meters squared