The base of right pyramid is an equilateral triangle, each side of which is 20 cm. Each slant edge is 30 cm. The vertical height (in cm) of the pyramid is:

Question

Question

This question was previously asked in

SSC CGL Tier 2 Quant Previous Paper 1 (Held On: 29 Jan 2022)

Answer 1

Given:

The base of right pyramid is an equilateral triangle, each side, (a) = 20 cm

Each slant edge, (E) = 30 cm

Concept used:

Circumradius of the equilateral triangle (r) = \(\frac{a}{{\sqrt 3}} \)

h = √(l² – r²)

Calculation:

F1 Savita SSC 12-4-22 D14

According to the question

Each side of an equilateral triangle = 20 cm

We know that, Circumradius of the equilateral triangle = \(\frac{a}{{\sqrt 3}} \)

⇒ AD = \(\frac{20}{{\sqrt 3}} \) cm

Now,

h = √(AE² – AD²)

h =√[30² – (\(\frac{20}{{\sqrt 3}})^2 \)]

⇒ h = √[(900 – \(\frac{400}{{3}}\))]

⇒ h = \(√ \frac{2700 - 400}{{3}}\)

⇒ h = \(√ \frac{2300}{{3}}\)

⇒ h = \(10√ {\frac{{23}}{3}} \) cm

∴ The vertical height of the pyramid is \(10√ {\frac{{23}}{3}} \) cm.