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

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, AB 2 = AD 2 + BD 2 .......(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, ⇒ 12 2 = AD 2 + 6 2 ⇒ 144 = AD 2 + 36 ⇒ AD 2 = 144 – 36 = 108 ⇒ AD = = 10.4 cm. Hence, area of triangle = 62.4 cm 2 and height = 10.4 cm.

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If the lengths of the sides of a triangle are in the ratio 3: 4 : 5 and its perimeter is 48 cm, find its area.

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Find the area of an equilateral triangle whose side is 8 m. Give your answer correct to two decimal places.

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Mathematics

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

Mensuration

Related Questions

If the lengths of the sides of a triangle are in the ratio 3: 4 : 5 and its perimeter is 48 cm, find its area.

Find the area of an equilateral triangle whose side is 8 m. Give your answer correct to two decimal places.