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*2AB*2AD [by eq(1) and eq(2)
= 2* area of the rectangle
thus area of the rectangle is half of the area of the rhombus.
hope this helps you