Answer:
Option 2nd is correct
[tex]41 ft^2[/tex]
Step-by-step explanation:
Similar states that two polygons are similar when their corresponding sides are in same proportion.
In a similar trapezoid, the area is proportional to the square of the side length.
As per the given statement:
Both trapezoids are similar.
The area of the smaller trapezoid is 26 square ft.
From the given figure:
Side of smaller trapezoid(a) = 16 ft
Side of larger trapezoid(b) = 20 ft
Let x be the the area of the larger trapezoid
By definition:
[tex]\frac{\text{Area of smaller trapezoid}}{\text{Area of larger trapezoid}} = \frac{a^2}{b^2}[/tex]
then;
[tex]\frac{26}{x} = \frac{16^2}{20^2}[/tex]
⇒[tex]\frac{26}{x} = \frac{256}{400}[/tex]
By cross multiply we have;
[tex]10400 = 256x[/tex]
Divide both sides by 256 we have;
40.625 = x
or
x ≈ 41 square ft
Therefore, the best approximation for the area of the larger trapezoid is, [tex]41 ft^2[/tex]
