If the perimeter of an equilateral triangle is 36 cm, calculate its area and height.
Mensuration
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Question

If the perimeter of an equilateral triangle is 36 cm, calculate its area and height.

KnowledgeBoat · Accepted Answer

We know that, Perimeter of an equilateral triangle = 3 × side. Substituting the values, ⇒ 36 = 3 × side ⇒ side = = 12 cm. Area of equilateral triangle = Substituting the values we get, From figure, In triangle ABD, Using Pythagoras Theorem, AB² = AD² + BD² .......(1) The perpendicular from a vertex of an equilateral triangle to the opposite side, bisects it. So, BD = = 6 cm. Substituting the values in (1) we get, ⇒ 12² = AD² + 6² ⇒ 144 = AD² + 36 ⇒ AD² = 144 – 36 = 108 ⇒ AD = = 10.4 cm. Hence, area of triangle = 62.4 cm² and height = 10.4 cm.

Mathematics

If the perimeter of an equilateral triangle is 36 cm, calculate its area and height.

Mensuration

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