Explanation:

Stress-Strain Curve:
The stress-strain curve is a graphical representation of the relationship between stress and strain in a material. It shows how the material deforms when subjected to an external force. The curve is obtained by plotting the stress (force per unit area) on the y-axis and the strain (change in length per unit length) on the x-axis.

Toughness:
Toughness is a measure of a material's ability to absorb energy without fracturing. It represents the area under the stress-strain curve up to the point of failure. The greater the area under the curve, the tougher the material is. Toughness is an important property in engineering applications as it indicates the material's ability to withstand impacts and sudden loads without breaking.

Breaking Strength:
Breaking strength refers to the maximum stress a material can withstand before it fractures or breaks. It is typically determined by the highest point on the stress-strain curve. However, the breaking strength alone does not provide information about the material's ability to absorb energy or its resistance to deformation.

Hardness:
Hardness is a measure of a material's ability to resist indentation or scratching. It is not directly related to the stress-strain curve or the area under it. Hardness is determined by performing specific tests such as the Rockwell or Brinell hardness tests.

Stiffness:
Stiffness, also known as modulus of elasticity, is a measure of a material's resistance to deformation under an applied load. It is determined by the slope of the stress-strain curve in the elastic region. Stiffness is not directly related to the area under the curve.

Therefore, the total area under the stress-strain curve of a mild steel specimen tested up to failure under tension is a measure of its toughness. The greater the area under the curve, the more energy the material can absorb before failure, indicating higher toughness.