The trapezoids are similar. The area of the smaller trapezoid is 564m^2. Find the area of the larger trapezoid to the nearest whole number.
The picture of the small one has a number 42m and the larger one has a number 57m.
Can someone please help me my possible answers aer, 576m^2, 3,249m^2, 3,181m^2, or 14m^2
reiny obviously if your answer doesn't match the answer choices you are wrong.
anyways the correct answer is 3,181 m^2
To find the area of the larger trapezoid, you can use the concept of similar triangles.
Since the trapezoids are similar, the corresponding sides of the trapezoids are proportional. In this case, the corresponding sides are the bases of the trapezoids.
The bases of the smaller trapezoid and the larger trapezoid have lengths of 42m and 57m, respectively.
To find the ratio of the areas of the two trapezoids, you need to square the ratio of the lengths of their corresponding sides.
In this case, the ratio of the bases is 57m/42m = 1.36 (rounded to two decimal places).
Now, you square this ratio: (1.36)^2 = 1.85 (rounded to two decimal places).
This means that the area of the larger trapezoid is approximately 1.85 times the area of the smaller trapezoid.
Given that the area of the smaller trapezoid is 564m^2, you can find the area of the larger trapezoid by multiplying this value by 1.85:
564m^2 * 1.85 ≈ 1044.6m^2
Rounding to the nearest whole number, the area of the larger trapezoid is approximately 1045m^2.
Therefore, the correct answer is not one of the options provided.
I will assume that the values of 42 m and 57 m are corresponding sides.
Areas of similar shapes are proportional to the square of their corresponding sides
A/564 = 57^2/42^2
A = 564(3249)/1764 = appr 1039 m^2
According to my assumption, none of the given answers match.
check: √(1039/564) = 1.357...
57/42 = 1.357...
my answer is correct.