The total amount reported for stockholders' equity is the approximate fair value or net worth of the corporation as of the balance sheet date, is it true?

yes TRUE!

True

The shareholders’ equity , or net worth , of a company equals the total assets (what the company owns) minus the total liabilities (what the company owes). If your company does well, its profits increase and its net worth increases too.Net worth = assets– liabilities = Shareholder's equity

actually strictly speaking the net worth of the business is the market value of the shares as at that date. and not merely their book values

True