# CBSE Class 9 Maths Chapter 12 : Heron’s Formula Solution, Pdf

What is a triangle?
The plane closed figure, with three sides and three angles is called as a triangle.

Types of Triangles (Based on the sides)

• Equilateral triangle
• Isosceles triangle
• Scalene triangle

Types of Triangles (Based on the sides)

• Acute angled triangle
• Obtuse angled triangle
• Right angled triangle

AREA OF TRIANGLE

Area of triangle or right angle triangle= ½baseheight

Area of equilateral triangle = √3a2/4

Area of isosceles triangle= (1/4) × b × √ (4a2 – b2)

AREA OF TRIANGLE BY HERON’S FORMULA

Area = √[s(s – a)(s – b)(s – c)]

Where s= (a+b+c)/2

Example– A triangle PQR has sides 4 cm, 13 cm and 15 cm. Find the area of the triangle.
Semi perimeter of triangle PQR, s = (4+13+15)/2 = 32/2 = 16 cm
By heron’s formula,
A = √[s(s-a)(s-b)(s-c)]
Hence, A = √[16(16-4)(16-13)(16-15)] = √(16 x 12 x 3 x 1) = √576 = 24 sq.cm

Example
The sides of triangle are a, a, a units

s=(a+ a+ a)/2​=3a/2​

Using Heron’s formula

Area of equilateral triangle is

Let ABCD he a quadrilateral to find the area of a quadrilateral we need to divide the quadrilateral in triangular parts

Here AB||CD and AC & BD are the diagonals.

Now we have two triangles here.
Area of quad ABCD = Area of ∆ADC + Area of ∆ABC (Calculate area of triangles by Heron’s formula)

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