Question

Find the slant height of a square pyramid with base edges of 12 cm and an altitude of 8 cm?

a) 12 cm
b) 9 cm
c) 10 cm
d) 11 cm

Answer 1

To find the slant height we must take apart the pyramid first. Let us cut it in half. There we can easily see that the slant height is really just the hypotenuse of the triangle formed by half the base and the altitude.

Half the base length would be 6 cm.

Using the Pythagorean therom:

a² + b² = c²
6² + 8² = c²
36 + 64 = c²
100 = c²
c = 10

The slant height should be 10 cm. Hope this helps!

Answer 2

The slant height of the square pyramid is 10 cm.

What is a square pyramid?

A Pyramid is a polyhedron that has a base and 3 or greater triangular faces that meet at a point above the base. A square pyramid is a pyramid with a square base, four triangular sides, five vertices, and eight edges.

For the given situation,

The base edge of the square pyramid = 12 cm

Altitude of the square pyramid = 8 cm

The diagram for the square pyramid is shown below.

To find the slant height, we need only the half of the base edge.

⇒ Half of  the base = 6 cm

Then, it looks like a right triangle. So we can find the slant height by using Pythagoras theorem.

The formula of Pythagoras theorem is

$Hypotenuse^{2}=base^{2} +perpendicular^{2}$

Here hypotenuse, h = slant height, l

base, b = 6 cm

perpendicular, p = 8

On substituting the above values,

⇒ $l^{2}=6^{2} +8^{2}$

⇒ $l^{2}=36+64$

⇒ $l^{2}=100$

⇒ $l=\sqrt{100}$

⇒ $l=10$

Hence we can conclude that the slant height of the square pyramid is 10 cm.

Learn more about square pyramid here

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