Answer:
[tex] PQ=4\sqrt{2} \:cm=5.66 \: cm[/tex]
Area of square PQRS[tex] = 32\: cm^2 [/tex]
Step-by-step explanation:
ABCD is a square. Points P, Q, R and S are the midpoints of sides AB, BC, CD and DA of square ABCD respectively.
Therefore,
BP = 1/2 * AB = 1/2 *8 = 4 cm
BQ = 1/2 * BC = 1/2 *8 = 4 cm
In [tex] \triangle PBQ, \: m\angle PBQ =90\degree [/tex]
Therefore, by Pythagoras theorem:
[tex] PQ=\sqrt{4^2 +4^2} [/tex]
[tex] PQ=\sqrt{2*4^2} [/tex]
[tex] PQ=4\sqrt{2} \:cm=5.66 \: cm[/tex]
Area of square PQRS[tex] =PQ^2 [/tex]
Area of square PQRS[tex] =(4\sqrt{2}) ^2 [/tex]
Area of square PQRS[tex] = 32\: cm^2 [/tex]
