# A rectangle is formed by joining the mid points of sides of a rhombus. Show that area of rectangle is half the area of the thombus.

it is given that PQRS is a rhombus. and A, B , C and D are the mid-points of the sides PQ, QR, RS and PS respectively.

therefore in the triangle PQR;

by the mid-point theorem AB = 1/2*PR .......(1)

and in the triangle PQS,

by mid-point theorem : AD=1/2*QS ......(2)

area of the rhombus = 1/2*product of the diagonals

=1/2* PR*QS

=1/2*2AB*2AD [by eq(1) and eq(2)

=2*AB*AD

= 2* area of the rectangle

thus area of the rectangle is half of the area of the rhombus.

hope this helps you

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