The diagonals AC and BD of a rhombus ABCD are 16 cm and 12 cm long, respectively. Calculate the area of the rhombus.
A
96 cm\(^2\)
B
36 cm\(^2\)
C
48 cm\(^2\)
D
24 cm\(^2\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Given that AC = 16 cm and BD = 12 cm. If O is the center. The diagonals of a rhombus meet at 90º.
AO = \(\frac{\text{AC}}{2}\) = 8cm;
BO = \(\frac{\text{BD}}{2}\) = 6 cm
AB\(^2\) = AO\(^2\) + OB\(^2\) (pythagoras theorem)
AB\(^2\) = 64 + 36 = 100;
AB = 10 cm
Area of △ABO = \(\frac{1}{2}\) \times 8 \times 6 = 24 cm\(^2\)
Area of rhombus = 4 \times area of △ABO ⇒ 4 \times 24 = 96 cm\(^2\).
Source: Myschool Past Questions Archive (Record #75832)