Questions
The figure below shows a parallelogram ABCD with BD=4 m and DC=5 m. Calculate the area of parallelogram ABCD.
detailed solution
Correct option is A
ΔADB is congruent to ΔDBC as the diagonal of a parallelogram divides it into two congruent triangles.
Now in right-angled triangle DBC:
∴ (BC)2 + (BD)2 = (DC)2 ..... (Pythagoras theorem)
∴ (BC)2 + 16 = 25
∴ (BC)2 = 25 - 16 = 9
∴ BC = 3 m
Now, Area of ΔDBC = × DB × BC
= × 4 × 3 = 6 m2
Since congruent triangles have equal areas
So, the area of ΔADB is also 6 m2
∴ Area of parallelogram ABCD = Area of ΔDBC + Area of ΔADB
= 6 + 6 = 12 m2
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