The trapezoids are similar. The area of the smaller trapezoid is 564 m². Find the area of the larger trapezoid to the nearest whole number.
two trapezoids are shown with the same orientation of parallel sides. The long base on the smaller triangle is 24 meters. The long base on the larger triangle is 57 meters.
(1 point)
Responses
576 m²
576 m²
3,249 m²
3,249 m²
3,181 m²
3,181 m²
14 m²
To find the area of the larger trapezoid, we can use the concept of similarity. Since the two trapezoids are similar, their corresponding sides are proportional.
The ratio of their long bases is given as 57 meters / 24 meters = 2.375.
Since the ratio of their corresponding sides is 2.375, the ratio of their areas would be the square of this ratio (since area is a 2-dimensional concept).
So, the area of the larger trapezoid would be (2.375)^2 times the area of the smaller trapezoid.
Area of larger trapezoid = (2.375)^2 * 564 m² = 3.249 * 564 m² ≈ 3,181 m²
Hence, the area of the larger trapezoid is approximately 3,181 m².