Question

The area of the figure formed by joining the mid points of the adjacent sides of a thombus with diagonals 16 cm and 12 cm is

• A. $28c{m}^2$
  
• B. $48c{m}^2$
  
• C. $96c{m}^2$
  
• D. $24c{m}^2$
  

Answer 1

The correct option is B

$48c{m}^2$

In rhombus ABCD,
P,Q,R and S are the mid points of sides AB, BC, CD and DA respectively and are joined in order to get a quad. PQRS.

Diagonals AC = 16 cm and BD = 12 cm
$\therefore$ Area of $PQRS=\frac{1}{2}$ area rhombus ABCD
$=\frac{1}{2}\times \frac{AC\times BD}{2}=\frac{1}{4}\times 16\times 12c{m}^2=48c{m}^2$