Question

The figure obtained by joining mid-point of adjacent sides of a rectangle of sides 8 cm and 6 cm is :

• A. a rectangle of area $24c{m}^2$
• B. a square of area $25c{m}^2$
• C. a trapezium of area$24c{m}^2$
• D. a rhombus of area $24c{m}^2$

Answer 1

The correct option is D a rhombus of area $24c{m}^2$

Using Pythagoras theorem, we can see that $SP=PQ=QR=RS=5$ units

Hence, $PQRS$ is a rhombus.

Ar(Rhombus) $=\frac{1}{2}($Product of Lengths of Diagonals$)$

Ar$\left(PQRS\right)=\frac{1}{2}\left(SQ\right)\left(PR\right)=\frac{1}{2}\left(8\right)\left(6\right)=24$ square units