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!

Accepted Solution

Answer:54 square metersStep-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 [tex]12k=18\\k=\frac{18}{12}\\k=1.5[/tex]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 Β [tex]k^2=(1.5)^2=2.25[/tex]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: Β [tex]x(2.25)=121\\x=\frac{121}{2.25}\\x=53.78[/tex]to nearest square meter, x = 54 meters squared