Question

iscoceles triangle frmula saayyyy

Answer 1

Step-by-step explanation:

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• b = base of the isosceles triangle
• h = height of the isosceles triangle
• a = length of the two equal sides

Derivation for Isosceles Triangle Area Using Heron’s Formula

The area of an isosceles triangle can be easily derived using Heron’s formula as explained below.

According to Heron’s formula,

Area = √[s(s−a)(s−b)(s−c)]

Where, s = ½(a + b + c)

Now, for an isosceles triangle,

s = ½(a + a + b)

⇒ s = ½(2a + b)

Or, s = a + (b/2)

Now,

Area = √[s(s−a)(s−b)(s−c)]

Or, Area = √[s (s−a)2 (s−b)]

⇒ Area = (s−a) × √[s (s−b)]

Substituing the value of “s”

⇒ Area = (a + b/2 − a) × √[(a + b/2) × ((a + b/2) − b)]

⇒ Area = b/2 × √[(a + b/2) × (a − b/2)]

Or, area of isosceles triangle = b/2 × √(a2 − b2/4)

Answer 2

Step-by-step explanation:

b = base of the isosceles triangle

h = height of the isosceles triangle

a = length of the two equal sides

Derivation for Isosceles Triangle Area Using Heron’s Formula

The area of an isosceles triangle can be easily derived using Heron’s formula as explained below.

According to Heron’s formula,

Area = √[s(s−a)(s−b)(s−c)]

Where, s = ½(a + b + c)

Now, for an isosceles triangle,

s = ½(a + a + b)

⇒ s = ½(2a + b)

Or, s = a + (b/2)

Now,

Area = √[s(s−a)(s−b)(s−c)]

Or, Area = √[s (s−a)2 (s−b)]

⇒ Area = (s−a) × √[s (s−b)]

Substituing the value of “s”

⇒ Area = (a + b/2 − a) × √[(a + b/2) × ((a + b/2) − b)]

⇒ Area = b/2 × √[(a + b/2) × (a − b/2)]

Or, area of isosceles triangle = b/2 × √(a2 − b2/4)