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

54 square meters

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=(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=(121)/(2.25)\\x=53.78`

to nearest square meter, x = 54 meters squared