Question

Both trapezoids are similar. The area of the smaller trapezoid is 26 ft2. Which is the best approximation for the area of the larger trapezoid?

25 ft2
41 ft2
49 ft2
33 ft2

Answer 1

Approximately 40.6 ft^2 so you round it to 41 ft^2.
So the answer is C.
Hope I am right! :)

Answer 2

Option 2nd is correct

`41 ft^2`

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:

`\frac{\text{Area of smaller trapezoid}}{\text{Area of larger trapezoid}} = (a^2)/(b^2)`

then;

`(26)/(x) = (16^2)/(20^2)`

⇒
`(26)/(x) = (256)/(400)`

By cross multiply we have;

`10400 = 256x`

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,
`41 ft^2`