3.In a parallelogram  ABCD, E  is the midpoint of  CD . Find the ratio between the area of  △ABE  and area of Parallelogram  ABCD .

Sure, here is the step by step solution:

Step 1: Understand the problem We have a parallelogram ABCD and E is the midpoint of CD. We need to find the ratio of the area of triangle ABE to the area of the parallelogram ABCD.

Step 2: Draw the figure Draw a parallelogram ABCD and mark E as the midpoint of CD. Draw a line from A to E.

Step 3: Find the area of triangle ABE The area of a triangle is 1/2 * base * height. In triangle ABE, base is AE and height is the perpendicular from B to AE. But in a parallelogram, the height (distance between the parallel sides) remains the same. So, the height of triangle ABE is the same as the height of the parallelogram.

Area of triangle ABE = 1/2 * AE * h

Step 4: Find the area of parallelogram ABCD The area of a parallelogram is base * height. Here, base is AD and height is the perpendicular from B or C to AD or BC.

Area of parallelogram ABCD = AD * h

Step 5: Find the ratio We need to find the ratio of the area of triangle ABE to the area of parallelogram ABCD.

Ratio = (Area of triangle ABE) / (Area of parallelogram ABCD) = (1/2 * AE * h) / (AD * h)

We know that in a parallelogram, opposite sides are equal. So, AE = AD.

Ratio = (1/2 * AD * h) / (AD * h) = 1/2

So, the ratio of the area of triangle ABE to the area of parallelogram ABCD is 1:2.