Question

The area of figure obtained by joining the midpoints of the adjacent sides of a rectangle of sides 8 cm and 6 cm is

• A. A rhombus of area $24c{m}^2$
  
• B. a rectangle of area $24c{m}^2$
  
• C. a square of area 26 cm^2
• D. a trapezium of area $14c{m}^2$
  

Answer 1

The correct option is A

A rhombus of area $24c{m}^2$

Let P, Q, R, S be the midpoints of sides of a rectangle ABCD whose sides 8 cm and 6 cm.

Then PQRS is a rhombus and ar$\left(PQRS\right)=\frac{1}{2}PR\times SQ=\frac{1}{2}\times 6\times 8=24c{m}^2$