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Question

If an isosceles triangle has perimeter 18 cm and base 8 cm, then its area is  cm2.
  1. 45 cm2
  2. 24 cm2
  3. 36 cm2
  4. 12 cm2


Solution

The correct option is D 12 cm2
Given: Perimeter of an isosceles triangle is 18 cm.
Let each of the equal sides of the isosceles triangle be x.
Then, 2x+8=18 x=5 cm
Hence, the sides are 5 cm, 5 cm and 8 cm.
Using the Heron's formula,
Area(A)=s(sa)(sb)(sc)
where s = semi-perimeter and a, b, c are the three sides of the triangle.
Semi-Perimeter (s)=Perimeter2
                        =182
                            =9 cm
A=9 (95)(95)(98)
=9×4×4×1
=144 cm2
=12 cm2

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