# Uniform plate of constant areal mass distribution

Diagram not to scale

The figure above shows a uniform plate in the shape of a cyclic quadrilateral $$ABCO$$ (with $$\angle B = \angle O = 90^{\circ}$$ and side lengths $$AB$$ and $$BC$$ as mentioned). It is given that the sides $$OC$$ and $$OA$$ are equal.

The mass of the plate is $$7 \text{ kg}$$ and its moment of inertia perpendicular to the plane of the plate and passing through its vertex $$O$$ can be expressed as $$84 \lambda \text{ kg cm}^2$$, where $$\lambda$$ is a positive constant. Find the value of $$\lambda$$.

×