Simplest way to get memory size of std::array's underlying array?

You can use the sizeof operator directly on your std::array instance:

sizeof(arr)

Example:

struct foo
{
    int a;
    char b;
};

int main()
{
    std::array<foo, 10> a;
    static_assert(sizeof(foo) == 8);
    static_assert(sizeof(a) == 80);
}

live example on wandbox

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From cppreference:

std::array is a container that encapsulates fixed size arrays.

This container is an aggregate type with the same semantics as a struct holding a C-style array T[N] as its only non-static data member.

There's no guarantee that sizeof(std::array<T,N>) == N*sizeof(T), but it is guaranteed that sizeof(std::array<T,N>) >= N*sizeof(T). The extra size might be named (but unspecified) members and/or unnamed padding.

The guarantee follows from the fact that the wrapped T[N] array must be the first member of std::array<T,N>, but other members aren't specified.