Final answer:
To find the area of a quadrilateral with a right angle between sides of lengths 5m and 12m, we calculate the area of the right-angled triangle formed, which is 30 square meters. For the entire quadrilateral's area, additional information about the shape is required.
Step-by-step explanation:
The area of a quadrilateral with sides of lengths 5, 12, 14, and 15 meters and a right angle between the first two sides can be calculated by dividing the quadrilateral into two triangles.
Since we have a right angle between the sides of length 5 meters and 12 meters, we can calculate the area of this right-angled triangle using the formula for the area of a triangle (1/2 * base * height). Therefore, the area of the right triangle is 1/2 * 5 * 12 = 30 square meters.
However, to find the area of the entire quadrilateral, we would need more information about the shape. If the quadrilateral is a rectangle, we could use the formula for the area of a rectangle (length * width).
If it's a trapezoid, we could use the formula for the area of a trapezoid. Since the question lacks details about the other angles or the relationship between the sides, we cannot provide a complete answer for the area of the entire quadrilateral. Assuming the figure is a kite or some other irregular quadrilateral, we would need additional details such as the diagonals' lengths or the other interior angles.