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Mathematics

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

Mensuration

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Answer

We know that,

Perimeter of an equilateral triangle = 3 × side.

Substituting the values,

⇒ 36 = 3 × side

⇒ side = 363\dfrac{36}{3} = 12 cm.

Area of equilateral triangle = 34(side)2\dfrac{\sqrt{3}}{4}(side)^2

Substituting the values we get,

A=34×(12)2=34×144=363=36×1.732=62.4 cm2A = \dfrac{\sqrt{3}}{4} \times (12)^2 \\[1em] = \dfrac{\sqrt{3}}{4} \times 144 \\[1em] = 36\sqrt{3} \\[1em] = 36 \times 1.732 \\[1em] = 62.4 \text{ cm}^2

From figure,

If the perimeter of an equilateral triangle is 36 cm, calculate its area and height. Mensuration, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

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 = 122\dfrac{12}{2} = 6 cm.

Substituting the values in (1) we get,

⇒ 122 = AD2 + 62

⇒ 144 = AD2 + 36

⇒ AD2 = 144 – 36 = 108

⇒ AD = 108\sqrt{108} = 10.4 cm.

Hence, area of triangle = 62.4 cm2 and height = 10.4 cm.

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