Question
Download Solution PDFThe perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Perimeter of Rhombus = 148 cm
One diagonal = 24 cm
Formula used:
Perimeter of Rhombus = 4 × side
Area of Rhombus = 1/2 × d1 × d2
where, d1 and d2 are diagonals of rhombus
Calculation:
Perimeter = 4 × side
⇒ 148 = 4 × side
⇒ side = 37 cm
In right angled triangle ΔAOB,
⇒ AB2 = AO2 + OB2
⇒ (37)2 = (12)2 + OB2
⇒ 1369 = 144 + OB2
⇒ OB2 = (1369 – 144)
⇒ OB2 = 1225 cm2
⇒ OB = 35 cm
BD = 2 × OB
⇒ 2 × 35 cm
⇒ 70 cm
Area of Rhombus = (1/2 × 24 × 70) cm2
⇒ 840 cm2
∴ Area of Rhombus is 840 cm2
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