If `E ,F ,G` and `H` are respectively the mid-points of the sides of a parallelogram `A B C D ,` show that `a r(E F G H)=1/2a r(A B C D)dot`

Explanation

To prove that the area of quadrilateral \(EFGH\) (formed by the midpoints of the sides of parallelogram \(ABCD\)) is half the area of parallelogram \(ABCD\), we can follow these steps:

### Step-by-Step Solution

1. **Identify Midpoints**: Let \(E\), \(F\), \(G\), and \(H\) be the midpoints of sides \(AB\), \(BC\), \(CD\), and \(DA\) of parallelogram \(ABCD\) respectively.

2. **Draw Diagonal**: Draw diagonal \(AC\) of parallelogram \(ABCD\). This diagonal divides the parallelogram into two triangles, \( \triangle ABC \) and \( \triangle ACD \).

...