Question

if the length of each edge of a regular tetrahedron is 'a' then the surface area is a)√3 a2 sq. units 2) 3√2 a2 sq. units 3) 2√3 a2 sq. units 4) √6 a2 units plz write it in steps​

Answer 1

Hey there,

Let a be the length of an edge of a regular tetrahedron. Then,

surface area = sum of the areas of three congruent equilateral triangles

= (√3) a² square units (option a)

HOPE this helps

thanks

Answer 2

Given:

Edge length of a regular tetrahedron = $a$ units

To find:

Surface area of the regular tetrahedron.

Solution:

A tetrahedron is a triangular pyramid consisting of four triangular faces, six edges and four vertices. It is given that the edge length of this tetrahedron is $a$ units. Then, the surface area of the tetrahedron is given by the formula,

$S=\sqrt{3}x^{2}$

where S is the surface area of the tetrahedron and $x$ is the length of the edges of the shape.

A regular tetrahedron is a tetrahedron having equal sides.

Here, the length of the edges of a regular tetrahedron is given as $a$ units,i.e., $x=a$.

Hence, the surface area of the tetrahedron is given by $\sqrt{3}a^{2} sq.units$. Thus, option (a) is the correct answer.

The surface area of a regular tetrahedron having side 'a' is given by $\sqrt{3}a^{2} sq.units$ and option (a) is the correct answer.