Find the area of Rhombus having each side equal to 17cm and one of its diagonal equal to 16cm
Answers
The area of Rhombus having each side equal to 17 cm and one of its diagonal equal to 16cm is 240 cm².
Step-by-step explanation:
Referring to the figure attached below,
Each side of the rhombus = 17 cm
One of the diagonal of rhombus ABCD , AC = 16 cm
Step 1:
We know that the two diagonals of any rhombus bisect each other at 90°.
∴ AO = OC = ½ * AC = ½ * 16 = 8 cm
And,
DO = OB = ½ * BD …… (i)
Now, applying Pythagoras theorem in ∆DOC, we get
DC² = OD² + OC²
⇒ 17² = OD² + 8²
⇒ OD = √ [289 – 64]
⇒ OD = √225
⇒ OD = 15 cm
Substituting the value of OD in (i), we get
BD = 2 * OD = 2 * 15 = 30 cm ← Second diagonal of the rhombus ABCD
Step 2:
Thus,
The area of the rhombus ABCD is given by,
= ½ * diagonal 1 * diagonal 2
= ½ * AC * BD
= ½ * 16 * 30
= 240 cm²
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