The figure below shows a parallelogram ABCD with BD=4 m and DC=5 m. Calculate the area of parallelogram ABCD.

# The figure below shows a parallelogram ABCD with BD=4 m and DC=5 m. Calculate the area of parallelogram ABCD. 1. A

12 m2

2. B

14 m2

3. C

15 m2

4. D

20 m2

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### Solution:

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 = $\frac{1}{2}$ ​× DB × BC

$\frac{1}{2}$ ​× 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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