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Question

Find the area of a figure formed by joining the midpoints of the adjacent sides of a rhombus with diagonals 12 cm and 16 cm.


Solution


Let ABCD be a rhombus and P, Q, R and S be the midpoints of AB, BC, CD and DA, respectively. 
Join the diagonals, AC and BD.
In ∆ ABC, we have:
PQ ∣∣ AC and PQ = 12AC                    [By midpoint theorem]
PQ=12×16=8 cm

Again, in ∆DACthe points S and R are the midpoints of AD and DC, respectively.
∴ SR ∣∣ AC and SR = 12AC                    [By midpoint theorem]
SR=12×12=6 cm
Area of PQRS=length×breadth=6×8=48 cm2

Mathematics
RS Aggarwal (2020, 2021)
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