Answer
Verified
439.8k+ views
Hint:
We shall first calculate the side of the equilateral triangle from its given height. Then using the side of the equilateral triangle, we will calculate its area.
Complete step by step solution:
We know that for an equilateral triangle of side $a$ and its height $h$ is given by,
$h = \dfrac{{\sqrt 3 }}{2}a$
The height given is $\sqrt 6 $ cm. So the side of the triangle can be evaluated as
$
\sqrt 6 = \dfrac{{\sqrt 3 }}{2}a \\
\Rightarrow a = 2\sqrt 2 \\
$
The side of the triangle is 2 cm.
Now we know that the area of the equilateral triangle of side $a$ is given by
$
Area = \dfrac{{\sqrt 3 }}{4}{a^2} \\
\Rightarrow Area = \dfrac{{\sqrt 3 }}{4}{(2\sqrt 2 )^2} \\
\Rightarrow Area = 2\sqrt 3 \\
$
So, the area of the given triangle is $2\sqrt 3 c{m^2}$.
Therefore, the correct option is B.
Note:
An equilateral triangle has all its sides and angles equal. The perpendiculars from each vertex acts as the perpendicular bisectors of the opposite sides. The intersection of these perpendiculars (or altitudes) is known as an orthocenter. The length of an altitude of an equilateral triangle is also its height.
We shall first calculate the side of the equilateral triangle from its given height. Then using the side of the equilateral triangle, we will calculate its area.
Complete step by step solution:
We know that for an equilateral triangle of side $a$ and its height $h$ is given by,
$h = \dfrac{{\sqrt 3 }}{2}a$
The height given is $\sqrt 6 $ cm. So the side of the triangle can be evaluated as
$
\sqrt 6 = \dfrac{{\sqrt 3 }}{2}a \\
\Rightarrow a = 2\sqrt 2 \\
$
The side of the triangle is 2 cm.
Now we know that the area of the equilateral triangle of side $a$ is given by
$
Area = \dfrac{{\sqrt 3 }}{4}{a^2} \\
\Rightarrow Area = \dfrac{{\sqrt 3 }}{4}{(2\sqrt 2 )^2} \\
\Rightarrow Area = 2\sqrt 3 \\
$
So, the area of the given triangle is $2\sqrt 3 c{m^2}$.
Therefore, the correct option is B.
Note:
An equilateral triangle has all its sides and angles equal. The perpendiculars from each vertex acts as the perpendicular bisectors of the opposite sides. The intersection of these perpendiculars (or altitudes) is known as an orthocenter. The length of an altitude of an equilateral triangle is also its height.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE