The area of the parallelogram is 360 square centimeters.
To find the area of the parallelogram, we can use the formula A = base × height, where the base is one of the consecutive sides and the height is the perpendicular distance between the two parallel sides. Given that the two consecutive sides of the parallelogram measure 32 centimeters and 15 centimeters and the included angle is 135°, we can use trigonometry to determine the height.
The height can be found by taking the sine of the given angle and multiplying it by the length of the shorter side (15 cm). So, height=15×sin(135∘). Once the height is determined, the area can be calculated as Area=base×height. After the computations, the area of the parallelogram is found to be 360 square centimeters.