Use familiar figures to find the area of each irregular figure.
Dotted lines divide an irregular shape into a square connected to the diagonal right side of a right trapezoid. The sides of the square measure 19 meters. The trapezoid has a short base of 24 meters, a long base of 30 meters, and a height of 18 meters.
An irregular figure has labeled side and angle measurements.
The area of the square is 19 meters x 19 meters = 361 square meters.
The area of the trapezoid is (24 + 30) x 18 / 2 = 270 square meters.
The total area of the irregular figure is 361 + 270 = 631 square meters.
To find the area of the irregular figure, we can break it down into familiar shapes and calculate their individual areas.
1. Start by finding the area of the square. Since all sides of the square measure 19 meters, the area can be calculated by multiplying the length of one side by itself: Area of square = (19 meters) x (19 meters) = 361 square meters.
2. Next, find the area of the trapezoid. The formula to calculate the area of a trapezoid is given by: Area of trapezoid = ((short base + long base) / 2) x height. Plugging in the given values, we have: Area of trapezoid = ((24 meters + 30 meters) / 2) x 18 meters = (54 meters / 2) x 18 meters = 972 square meters.
3. Finally, find the total area of the irregular figure by adding the areas of the square and the trapezoid: Total area = Area of square + Area of trapezoid = 361 square meters + 972 square meters = 1333 square meters.
Therefore, the area of the irregular figure is 1333 square meters.