In a rectangle ABCD, if X and Y are the midpoints of sides AB and BC respectively, find the ratio of the area of triangle DXY and that of the rectangle.

Sure, here are the steps to find the ratio of the area of triangle DXY to that of the rectangle ABCD:

Step 1: Understand the problem We have a rectangle ABCD. X and Y are the midpoints of sides AB and BC respectively. We need to find the ratio of the area of triangle DXY to that of the rectangle ABCD.

Step 2: Draw the rectangle and the triangle Draw the rectangle ABCD. Mark the midpoints X and Y on sides AB and BC respectively. Draw the triangle DXY.

Step 3: Find the area of the rectangle The area of a rectangle is given by the formula length * breadth. Let's assume the length of the rectangle is 'a' and the breadth is 'b'. So, the area of the rectangle ABCD is a*b.

Step 4: Find the area of the triangle The area of a triangle is given by the formula 1/2 * base * height. In triangle DXY, DX is the base and XY is the height. Since X and Y are midpoints, XY is half the length of the rectangle, which is a/2. DX is the same as the breadth of the rectangle, which is b. So, the area of triangle DXY is 1/2 * b * a/2 = a*b/4.

Step 5: Find the ratio The ratio of the area of triangle DXY to that of the rectangle ABCD is (ab/4) / (ab) = 1/4.

So, the ratio of the area of triangle DXY to that of the rectangle ABCD is 1:4.