Question

If the diagonals of a rhombus ABCD intersect at O such that AO = 6 cm and BO = 4 cm, find the area of the rhombus ABCD

• A. 88 cm${}^2$
• B. 48 cm${}^2$
• C. 56 cm${}^2$
• D. 76 cm${}^2$

Answer 1

The correct option is B 48 cm${}^2$

Given: AO = 6 cm and BO = 4 cm

We know that diagonals of rhombus bisect each other.
So, AC = 2AO and BD = 2BO.
AC = 2(6) = 12 cm
BD = 2(4) = 8 cm

Area of the rhombus = $\frac{1}{2}\times$ Product of the diagonals
Area of the rhombus ABCD = $\frac{1}{2}\times AC\times BD$
Area of the rhombus ABCD = $\frac{1}{2}\times 12\times 8$
Area of the rhombus ABCD = 48 cm${}^2$