16) Each side of an equilateral triangle measures 9 cm. Find:
(a) The area of a triangle to 2 places of decimal
(b) The height of the triangle , correct to 2 places of decimal. Take √3 = 1.732
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suhanithakur50p7n5rg
23.04.2018
Math
Secondary School
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The height of the equilateral triangle measures 9 cm find its area correct to 2 places of decimal
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ArchitectSethRollins
ArchitectSethRollins Ace
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
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Panzer786
Panzer786 Genius
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..... :-)