The sides of a parallelogram are 100 m each and length of the longest diagonal is 160m. The area of a parallelogram is.?

Question

Answer

Solution:

Given:

Sides of parallelogram = 100m each

Length of longest diagonal = 160m

Concept:
In a parallelogram, opposite sides are equal in length and opposite angles are equal in measure. Also, the diagonals bisect each other.

Steps:

Let ABCD be a parallelogram with sides AB and BC of length 100m each.

Let BD be the longest diagonal of the parallelogram of length 160m

Draw altitude BE from B to CD, which divides parallelogram ABCD into two right triangles ABE and BCE.

Since AB = BC and BE is perpendicular to CD, we have CE = ED = 50m.

Using the Pythagorean theorem, we can find the length of BE as:

$(BE)^2 = (AB)^2 - (AE)^2$

$(BE)^2 = (100)^2 - (50)^2$

$(BE)^2 = 7500$

$BE = \sqrt{7500} = 50\sqrt{3}$

The area of parallelogram ABCD can be found as:

Area = base x height

Area = AB x BE

Area = 100m x $50\sqrt{3}$m

Area = $5000\sqrt{3}$ sq.m

Answer:
The area of parallelogram ABCD is $5000\sqrt{3}$ sq.m.

Answer

9600 meters

Answer

9600 m²

Answer

Area of Parallelogram is 9600 m .

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