Question

The square pyramid shown below has a base with sides of 10 units. The slant height of the pyramid is 8 units. What is the vertical height, h?

Answer 1

6.2

Explanation:

We can use the Pythagorean Theorem to find h.

The equation for the Pythagorean Theorem is a^2+b^2=c^2

We see that the hypotenuse of the right triangle is 8. One leg is h. The other leg is 5 , which is half the length of the base.

We have:

a^2+b^2=c^2

5^2+h^2=8^2

25+h^2=64

h^2=39

h= square root of 39

h = 6.244

6.2

Answer 2

Make a right triangle by using half the base and using the Pythagorean theorem calculate the height.

Height = sqrt(8^2 - 5^2)

Height = sqrt(64 - 25)

Height = sqrt(39)

Height = 6.245 ( Round the answer as needed).