Question

Semi-perimeter of an isosceles triangle, whose base is 12cm and each of its equal side is 8cm will be? *

Answer 1

Required Answer :

The semi perimeter of the isosceles triangle = 14 cm

Given :

• Base of an isosceles triangle = 12 cm
• The two equal sides of the isosceles triangle = 8 cm

To find :

• Semi - perimeter of the isosceles triangle

Solution :

Here, we are given the three sides of an isosceles triangle i.e, 12 cm, 8 cm and 8 cm and we need to calculate the semi perimeter. To find the semi perimeter, we will be using the following formula :

• Semi - perimeter = (a + b + c) ÷ 2

or

• Semi - perimeter = Perimeter ÷ 2

where,

• a denotes the first side of the triangle
• b denotes the second side of the triangle
• c denotes the third side of the triangle

we have,

• a = 12 cm
• b = 8 cm
• c = 8 cm

Substituting the given values :

⇒ Semi perimeter = (12 + 8 + 8) ÷ 2

⇒ Semi perimeter = 28 ÷ 2

⇒ Semi perimeter = 14

Therefore,

• The semi perimeter of the isosceles triangle = 14 cm

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Some related formulae :

• Area of isosceles triangle = ½ × b × h
• Perimeter = Sum of all sides
• Heron's formula = √s(s - a)(s - b)(s - c)
• Area of equilareral triangle = √3/4 a

where,

• s denotes the semi perimeter
• a denotes the side of the triangle
• b denotes the base
• h denotes the height