Question

ABCD is a square of area $1m^2$ P and Q are the midpoints of AB and BC respectively What is the area of $\Delta DPQ?$

• A. $\frac{3}{8}{m}^2$
• B. $\frac{5}{8}{m}^2$
• C. $\frac{5}{4}{m}^2$
• D. $\frac{3}{4}{m}^2$

Answer 1

The correct option is A $\frac{3}{8}{m}^2$

$\text{Area of}\Delta DPQ=\text{Area of square}ABCD-\text{Area of}\Delta APD$ $-\text{Area of}\Delta BPQ$ $-\text{Area of}\Delta DQC$$=1-(\frac{1}{2}\times AP\times AD)-(\frac{1}{2}\times BP\times BQ)-(\frac{1}{2}\times QC\times DC)$
$=1m^2-(\frac{1}{2}\times \frac{1}{2}\times 1)m^2-(\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2})m^2-$$(\frac{1}{2}\times \frac{1}{2}\times 1)m^2$
$=(1-\frac{1}{4}-\frac{1}{8}-\frac{1}{4})m^2$ $=(1-\frac{5}{8})m^2=\frac{3}{8}{m}^2$