What is the area of the figure below?
A quadrilateral is shown with its diagonals.The top left and right sides of the quadrilateral are congruent.
The lower left and right sides of the quadrilateral are also congruent.
The angle formed at the top vertex by the diagonal and the top left side is 45 degrees.
The segment from the top vertex to the diagonal intersection is 2.5 meters.
The segment from the diagonal intersection to the bottom vertex is 6 meters.
(1 point)
Responses
7.5 m²
7.5 m²
15 m²
15 m²
21.25 m²
21.25 m²
42.5 m²
The area of the quadrilateral can be split into two triangles.
The area of the triangle formed by the top vertex, diagonal intersection, and top right side is (1/2) * 2.5 * 6 * sin(45°) = 3.5355 m².
The area of the triangle formed by the diagonal intersection, bottom vertex, and bottom right side is (1/2) * 6 * 6 = 18 m².
Therefore, the total area of the quadrilateral is 3.5355 m² + 18 m² = 21.5355 m², which is closest to 21.25 m².
So, the area of the figure is approximately 21.25 m².