Question

the height of the equilateral triangle measures 9 cm find its area correct to 2 places of decimal

Answer 1

Hi friend
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Your answer
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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.)

HOPE IT HELPS

Answer 2

Hii friend,

Let each side of an equilateral triangle be X cm.

Height of an equilateral triangle = 9 cm

✓3/2 × Side = 9

✓3/2×X = 9

X = 9×2/✓3

X = 18/✓3 ×✓3/✓3

X = 18✓3/3

X = 6✓3 cm

Side of an equilateral triangle = X = 6✓3 cm

Therefore,

Area of an equilateral triangle = ✓3/4 × Side²

=> ✓3/4 × (6✓3)²

=> ✓3 /4 × 36 × 3

=> ✓3/4 × 108

=> ✓3 × 27

=> 27✓3 CM²

=> 27×173/100

=> 4671/100

=> 46.71 cm².


Hence,

The area of an equilateral triangle correct to 2 place of decimal is 46.71 cm²


HOPE IT WILL HELP YOU..... :-)