Question

If EFGH is a parallelogram with P and Q as mid points of sides GH and EF respectively , then show that area used for first aid is half the total area​

Answer 1

Area of HPFQ = 1/2 (Area of EFGH)    

Parallelogram = EFGH (Given)

Let,  EF = HG = x ( In parallelogram opposite sides are always equal in size)

Let the height of EFGH = h

Let height of HPFQ = H  ( As HPFQ lies between the same parallel sides as EFGH)

​Therefore,

Area of parallelogram EFGH = (Height × base)

= hx --- eq 1  

​Since, Q and P are the mid points of the EF and GH.

Thus,

QF = HP = x/2

Area of HPFQ = hx/2 --- eq 2                                          

From equation 1 and 2 we will get

Area of HPFQ = 1/2 (Area of EFGH)                              

Hence Proved.