What is the area of the figure below? 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 42.5 m²
To find the area of the quadrilateral, we need to split it into two triangles and find the area of each triangle separately.
First, let's find the area of the top triangle:
Since the angle formed at the top vertex by the diagonal and the top left side is 45 degrees, we have a right triangle with one leg being 2.5 meters and the angle being 45 degrees. Using the trigonometric properties of right triangles, we can calculate the length of the other leg (let's call it x) as x = 2.5 * tan(45) = 2.5.
So, the area of the top triangle is 0.5 * 2.5 * 2.5 = 3.125 m²
Next, let's find the area of the bottom triangle:
We have a right triangle with one leg being 6 meters and the angle being 90-45=45 degrees. Using the trigonometric properties of right triangles, we can calculate the length of the other leg as x = 6 * tan(45) = 6.
So, the area of the bottom triangle is 0.5 * 6 * 6 = 18 m²
Therefore, the total area of the quadrilateral is the sum of the areas of the two triangles, which is 3.125 + 18 = 21.125 m².
So, the correct answer is 21.25 m².