Question

Find the area of a rhombus,each side of which measures 20cm and one of whose diagonal is 24 cm.

Answer 1

Hey!

♣ QUADRILATERALS ♣

Given, one side = 20 cm
And one diagonal = 24 cm

We know,
Pythagorean Theorem!
H² = B² + P²
(AB)² = (OA)² + (OB)²
(20)² = (OA)² + (12)²
400 = (OA)² + 144
400 - 144 = (OA)²
256 = (OA)²
16 cm = OA
Then,
AC = 2 x 16 
      = 32cm

Now, Area = 1/2× product of its diagonals
=1/2×24×32
=384cm^2

Thanks,

Niki..... :-)

Answer 2

Heya !!




Let ABCD is a rhombus , in which AD and BC are it's two diagonals.




AB = AC = CD = BD = 20 cm.



Let AD = 24 cm.






Therefore,


OA = 1/2 × AB = 1/2 × 24 = 12 cm.




And,



AB = 20 cm.




In right angled triangle OAB,





OB² = (AB)² - (OA)²



OB² = (20)² - (12)²




OB = √256 = 16 cm.






Therefore,



BC = 2 × OB = 2 × 16 = 32 cm.




Area of rhombus ABCD = 1/2 × ( AD × BC )




=> 1/2 × ( 24 × 32 )




=> 768/2



=> 384 cm².