Topics Covered

8 key topics in this chapter

Heron's Formula for Area

Semi-perimeter s = (a+b+c)/2

Area of Scalene Triangle

Area of Equilateral Triangle

Quadrilateral Area via Triangles

Triangular Plots & Fields

Area in Terms of Sides Only

Applications in Surveying

Study Resources

Formula / Rule	Expression
Heron's Formula	\(A = √[s(s−a)(s−b)(s−c)]\)
Semi-perimeter	\(s = (a + b + c) / 2\)
Equilateral △	\(A = (√3/4)a²\)
Isosceles △ (base b, equal sides a)	\(A = (b/4)√(4a²−b²)\)
Right △	\(A = ½ × base × height\)
Quadrilateral via triangles	\(A = A₁ + A₂ (diagonal divides into 2 △s)\)

Semi-perimeter s = (a + b + c) / 2. Heron's formula gives area without needing the altitude — useful for scalene triangles.

For an equilateral triangle with side a: Area = (√3/4)a². This follows directly from Heron's with a = b = c.

For a quadrilateral, divide it into two triangles using a diagonal, apply Heron's formula to each, and add the areas.

Always check units: if sides are in cm, area is in cm². If metres, area in m².