Question

A triangular field has sides of lengths 19, 31, 43 m.
Find the area of the triangular field:

Answer 1

To calculate the area of a triangular field with sides measuring 19 m, 31 m, and 43 m, Heron's formula is used after finding the semi-perimeter. The area is the square root of the product of the semi-perimeter and the semi-perimeter minus each side's length.

Step-by-step explanation:

The area of a triangular field with sides of lengths 19 m, 31 m, and 43 m can be calculated using Heron's formula. Firstly, calculate the semi-perimeter (s) of the triangle, which is the sum of all sides divided by 2:

s = (19 + 31 + 43) / 2 = 46.5 m

Then, apply Heron's formula to find the area (A):

A = √[s(s - 19)(s - 31)(s - 43)]

Substituting the known values gives us:

A = √[46.5(46.5 - 19)(46.5 - 31)(46.5 - 43)]
A = √[46.5 × 27.5 × 15.5 × 3.5]

The exact area calculation would involve multiplying these values together and taking the square root of the result. However, without a calculator, we can conclude that the area of the triangular field in square meters will be the square root of the given product, which can then be rounded to an appropriate number of significant figures.

Answer 2

In order to determine the area of a triangular field, Heron's formula is applied. This involves first calculating the semi-perimeter of the triangle (half the sum of its three sides) and then using it in Heron's formula, which employs the square root function on the product of the semi-perimeter and its differences with each side of the triangle.

Step-by-step explanation:

The question asks to find the area of a triangular field with side lengths of 19 m, 31 m, and 43 m.

To calculate the area of a triangle when three sides are given, one can use Heron's formula.

Heron's formula states that the area (A) of a triangle can be calculated from its three sides a, b, and c using the formula:

A = √[s(s-a)(s-b)(s-c)]

where s represents the semi-perimeter of the triangle, which is calculated as half the sum of the sides:

s = (a+b+c) / 2

For the triangular field with sides 19 m, 31 m, and 43 m:

s = (19 + 31 + 43) / 2 = 46.5 m

Then, the area A is calculated as:

A = √[46.5(46.5-19)(46.5-31)(46.5-43)]

After evaluating the square root and the multiplications inside it, we find the area of the triangle.