Question

find the area of the Rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm​

Answer 1

SOLUTION:-

➡️Let A, B, C and D be the vertices of the rhombus. 

The diagonals of a rhombus will be perpendicular and they will bisect each other. 

Then, we have

➡️In the above rhombus, consider the right angled triangle BDE. 

By Pythagorean Theorem, 

BD²  =  BE² + DE²

17²  =  BE² + 8²

289  =  BE² + 64

➡️Subtract 64 from each side. 

225  =  BE²

15²  =  BE²

15  =  BE

Then, 

EC  =  15

➡️Length of the diagonal BC : 

BC  =  BE + EC

BC  =  15 + 15

BC  =  30 units

So, the lengths of the diagonals are 16 units and 30 units. 

➡️Formula for area of a rhombus :

=   1/2 ⋅ (d1d2)

➡️Substitute 16 for d1 and 30 for d2.

=   1/2 ⋅ (16 ×30)

=   8 × 30

=  240 

➡️So, area of the rhombus is 240 square units.