THE HEIGHT OF AN EQUILATERAL TRIANGLE IS 6 CM CIND ITS AREA.
YASH3100:
Well hello there, see I'll not be able to give the full answer over here but I'll just tell you how to solve it, so listen it's a property of an equilateral triangle that altitude from any of its vertex to the other side, bisects the side i.e the altitude acts as a median as well (only in case of equilateral triangle)
Now in the triangle made by one of the side, the bisected side and the altitude
Let the length of the side be x therefore the bisected side will be x/2 and x/2 so in that triangle apply Pythagoras theorem
As the altitude is given to be 6cm and the Two sides are x cm and x/2 cm
So apply Pythagoras theorem to calculate the value of x
So you'll get the length of the side as √48 cm now apply the area formula for an equilateral triangle to find the area.
thanku
Hope you get it although I know it would be a bit difficult to imagine but if you get any doubt pls feel free to ask
Answers
Answered by
10
Hey!
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 !
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 !
Answered by
3
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
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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