Question

What is the slant height x of the square pyramid?

Express your answer in radical form.

Answer 1

The slant height of square pyramid = 4√3 m

Explanation:

From the figure we can see a square pyramid with lateral edge 8 m

Also the one angle of face triangle is 60° , therefore the face triangle is an equilateral triangle.

Therefore the base is 8 m

To find the slant height

slant height² = Lateral edge² - (base/2)²

= 8² - (8/2)² = 8² - 4²

= 64 - 16 = 48

Slant height = √48 = 4√3 m

Therefore slant height of square pyramid = 4√3 m

Answer 2

x =
`4 \sqrt { 3 }`

Explanation:

We are given a diagram of a pyramid with a right angled triangle which has
`30`°,
`60`° and
`90`° angles an the hypotenuse is
`8cm`.

Since we have a right angled triangle, we can apply sin here:

We know that
`sin 60 = (√(3) )/(2)` so we can write it as

`(√(3) )/(2) = (x)/(8)`

So we get the slant height of x =
`4√(3)`.