Question

A right square pyramid is shown. The base has a side length, b, of 30 centimeters (cm). The height, h, is 10 cm.

What is the length, in centimeters, of l?

Draw and label a triangle to model how to find the length of l.
What are the lengths of the legs? How do you know?







What is the length, in centimeters, of l? Use your model to help you find this value.

Answer 1

Explanation:

Without the illustration, I assume that L is the slant height of a triangular face.

L = √(15^2 + 10^2) = 5√13 cm

Answer 2

The length of l is 15√2 cm.

The length of the height is 10 cm.

To find the length of l, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is l, and the other two sides are the height of the pyramid (10 cm) and half of the base side length (30 cm / 2 = 15 cm).

Therefore, we have the following equation:

l² = 10² + 15²

l² = 225 + 225

l² = 450

l = √450

l = 15√2 cm

Therefore, the length of l is 15√2 cm.

Diagram:

[Diagram of a right square pyramid with the height (10 cm) and half of the base side length (15 cm) labeled. The hypotenuse (l) is also labeled.]

Lengths of the legs:

The length of the height is 10 cm. The length of half of the base side length is 30 cm / 2 = 15 cm.

How do we know the lengths of the legs?

The height of the pyramid is given in the question. The length of half of the base side length is calculated by dividing the base side length by two.

Finding the length of l:

We can use the Pythagorean Theorem to find the length of l, as shown above.