A triangle has a base length of 3.1 cm and corresponding height of 4.2 cm, correct to one decimal place. Calculate the upper and lower bounds for the area of the triangle as
accurately as possible.

The upper bound of the area is 6.69375 cm²

The lower bound of the area is 6.32875 cm²

Step-by-step explanation:

The question relates to measurements and accuracy

The given information are;

The base length of the triangle = 3.1 cm

The height of the triangle = 4.2 cm correct to one decimal place

The lower bound for the base length of the triangle = 3.05 cm

The upper bound for the base length of the triangle = 3.15 cm

Similarly, the lower bound for the height of the triangle = 4.15 cm

The upper bound for the height of the triangle = 4.25 cm

The formula for calculating the area of a triangle is given by the following formula;

Area of a triangle = 1/2 × Base × Height

The upper bound of the area = 1/2 × The upper bound of the base × The upper bound of the height

The upper bound of the area = 1/2 × 3.15 × 4.25 = 6.69375 cm²

The upper bound of the area = 6.69375 cm²

The lower bound of the area = 1/2 × The lower bound of the base × The lower bound of the height

∴ The lower bound of the area = 1/2 × 3.05 × 4.15 = 6.32875 cm²

The lower bound of the area = 6.32875 cm²