Question

The base of a solid oblique pyramid is an equilateral triangle with an edge length of s units.

Answer 1

The base of a solid oblique pyramid is an equilateral triangle with an edge length of s units.
Which expression represents the height of the triangular base of the pyramid?

5/2 √3 units

Answer 2

Answer:

Option B is correct.i.e.,

Step-by-step explanation:

Given: Pyramid with equilateral triangle as base

           Length of side of equilateral triangle = s unit

to find: height of equilateral triangle

Here we use a property of equilateral triangle.

Perpendicular from a vertex on a side and median of that side of a triangle is same in equilateral triangle.

All heights are of equal length. So, we just need to find one height or length of 1 altitude.

Figure of base triangle is attached

In Δ ABC

AB = BC = AC = s unit

AD is height

BD = $\frac{BC}{2}\:=\:\frac{s}{2}\:units$

Now, In Δ ABD

using pythagoras theorem

BD² + AD² = AB²

$(\frac{s}{2})^2+AD^2=s^2$

$\frac{s^2}{4}+AD^2=s^2$

$AD^2=s^2-\frac{s^2}{4}$

$AD^2=\frac{4s^2-s^2}{4}$

$AD^2=\frac{3s^2}{4}$

$AD=\sqrt{\frac{3s^2}{4}}$

$AD=\frac{\sqrt{3}s}{2}$

$AD=\frac{s}{2}\sqrt{3}$

Therefore, Option B is correct.i.e., $\frac{s}{2}\sqrt{3}$