Question

Which statement is true about the figure formed by joining the midpoints of the adjacent sides of a rectangle with sides $8cm$ and $6cm$?

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

Answer 1

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

R.E.F image

As $\left(PBQ\right);\left(RCQ\right);\left(APS\right)$

& $\left(SRD\right)$ are Rt. triangle

& $DR=RC=AP=PB=4$

& $DS=SA=QB=QC=3$

$\Rightarrow SR=PS=PQ=RQ=\sqrt{3^2+4^2}$

$=5units$

As all side are eqval &

angle is not necessary

${90}^{\circ }\therefore$ it is a phombus

with area $=\frac{1}{2}\times RP\times SQ$

$\Rightarrow ar\left(PQRS\right)=\frac{1}{2}\times 8\times 6=24$