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

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

Related Questions

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

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.