The formula for calculating the height of an equilateral triangle = a√3 / 2 units.
So Height = 6 cm
=> 6 = a√3 / 2
=> 6 * 2 = a√3
=> 12 = a√3
=> a = 12 / √3
=> a = 12 √3 / 3
=> a = 4√3 units.
So Side of the triangle = 4 √3 units.
Area of equilateral trinagle = 1 / 2 × base × height
=> Area = 1 / 2 × 4 √3 × 6
=> Area = 6 / 2 × 4 √3
=> Area = 3 × 4 √3
=> Area = 12 √3 units
Hope it helped !
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Shubhendu8898
Given height (h) = 6cm Draw a equilateral triangle (see picture) let the sides of traingle be 2x. Draw a perpendicular on base as shown in picture. Applying Pythagoras theorem in traingle ABD We get, (2x)² = h² + x²
4x² = 6² + x²
3x²= 36
x²= 12
x=√12cm
Hence, Area of triangle = 1/2* base× height = 1/2 ×(2x) ×h =x*h =6√12 = 6×2√3 = 12√3cm²
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Solution :
The formula for calculating the height of an equilateral triangle = a√3 / 2 units.
So Height = 6 cm
=> 6 = a√3 / 2
=> 6 * 2 = a√3
=> 12 = a√3
=> a = 12 / √3
=> a = 12 √3 / 3
=> a = 4√3 units.
So Side of the triangle = 4 √3 units.
Area of equilateral trinagle = 1 / 2 × base × height
=> Area = 1 / 2 × 4 √3 × 6
=> Area = 6 / 2 × 4 √3
=> Area = 3 × 4 √3
=> Area = 12 √3 units
Hope it helped !
height (h) = 6cm
Draw a equilateral triangle (see picture)
let the sides of traingle be 2x.
Draw a perpendicular on base as shown in picture.
Applying Pythagoras theorem in traingle ABD
We get,
(2x)² = h² + x²
4x² = 6² + x²
3x²= 36
x²= 12
x=√12cm
Hence,
Area of triangle = 1/2* base× height
= 1/2 ×(2x) ×h
=x*h
=6√12
= 6×2√3
= 12√3cm²