The total area of a trapezoid is 288 cm².
To find the area of the trapezoid, we need to divide it into two triangles and a rectangle.
Let's start with the rectangle.
The base of the rectangle is AB, which is 15 cm, and its height is MN, which is 15 cm.
So, the area of the rectangle is 15 cm * 15 cm = 225 cm².
Now let's calculate the area of the two triangles. The first triangle has base BA and height DM, which are both 15 cm.
So, the area of the first triangle is 15 cm * 3 cm * 1/2 = 22.5 cm².
The second triangle has base AB, which is 15 cm, and height CN, which is 3 cm. So, the area of the second triangle is 15 cm * 3 cm * 1/2 = 22.5 cm².
Now, we can find the total area of the trapezoid by adding the areas of the rectangle and the two triangles. 225 cm² + 22.5 cm² + 22.5 cm² = 288 cm².
Therefore, the area of trapezoid A is 288 cm².
The probable question may be:
In a trapezoid ABCD a line is drawn from point A on side CD as AM =16cm, a line is drawn from point B on side CD as BN, Side Ab=15cm, side CN=3cm, MN=15cm, DM=3cm, Find the area of trapezoid
A. 240cm^2
B. 288cm^2
C. 312cm^2
D. 336cm^2