Question

The height of a equilateral triangle measures 9 CM find its area, correct to two 2 places of decimals.

Answer 1

Answer:

Heya!

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There you go

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Height of an equilateral triangle = 9 cm

Now,

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√3/2 × side = Height

√3/2 × side = 9

=> side = (9 × 2)/√3

=> Side = 3√3 × 2 = 6√3 cm

Again,

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Area = √3/4 × (side)²

= [√3/4 × 6√3 × 6√3] cm²

= 27√3 cm²

= (27 × 1.732) cm² [Taking √3 = 1.732]

= 46.764 cm²

= 46.76 cm² (correct to 2 decimal places.)

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Step-by-step explanation:

Answer 2

Answer:

Consider a as the side of an equilateral triangle We know that Height of an equilateral triangle = √3/2 a

It is given that height = 9cm So we get √3/2 a = 9

On further calculation a = (9 × 2)/ √3

Multiplying both numerator and denominator by √3 We get

a = (9 × 2 × √3) / (√3 × √3)

So we get Base = a = 6√3cm

We know that the area of an equilateral triangle = ½ × b × h

By substituting the values Area of the equilateral triangle = ½ × 6√3 × 9

On further calculation Area of the equilateral triangle = 27√3 cm2

By substituting the value of √3

Area of the equilateral triangle

= 27 × 1.732 = 46.764

By correcting to 2 places of decimal Area of the equilateral triangle = 46.76 cm2

Therefore, the area of an equilateral triangle = 46.76 cm2.