Using Heron's Formula to Find the Area of an Equilateral Triangle with Side 7 Metres

Definition: Heron's formula is a mathematical formula used to calculate the area of a triangle when the length of all three sides are known.

Equilateral Triangle: An equilateral triangle is a triangle in which all three sides are equal.

Formula: Heron's formula is given by:

Area = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle and is given by:

s = (a+b+c)/2

and a, b, and c are the lengths of the three sides of the triangle.

Steps to Find the Area of an Equilateral Triangle with Side 7 Metres:

1. Determine the length of each side of the equilateral triangle. Since all sides of an equilateral triangle are equal, the length of each side is 7 metres.

2. Calculate the semi-perimeter of the triangle using the formula:

s = (a+b+c)/2

Since all three sides are equal, we can substitute 7 for a, b, and c:

s = (7+7+7)/2
s = 10.5

3. Use Heron's formula to calculate the area of the triangle:

Area = √(s(s-a)(s-b)(s-c))

Substitute 7 for a, b, and c, and 10.5 for s:

Area = √(10.5(10.5-7)(10.5-7)(10.5-7))
Area = √(10.5(3.5)(3.5)(3.5))
Area = √(105.875)
Area = 10.3 square metres (rounded to one decimal place)

Conclusion: The area of an equilateral triangle with side 7 metres using Heron's formula is 10.3 square metres.