What is the reason for an element in the Serendipity family to have a smaller size of stiffness matrix compare to a similar element in the Lagrange family?

What is the reason for an element in the Serendipity family to have a smaller size of stiffness matrix compare to a similar element in the Lagrange family? Correct Answer Absence of interior nodes

The internal nodes of the higher-order elements of the Lagrange family do not contribute to inter-element connectivity, and hence they are condensed out at element level; as a result, the size of the element matrices is reduced. However, the element connectivity remains unaffected. The elements formed after removing the internal nodes are called serendipity elements.
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The correct answer is
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