Question

Math

Posted 5 months ago

```
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, $h$ ?
Round your answer to the nearest tenth.
The height is $\square$ units.
```

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Answer from Sia

Posted 5 months ago

Solution by Steps

step 1

Given the right triangle within the pyramid, we use the Pythagorean theorem $a^2 + b^2 = c^2$, where $a$ and $b$ are the legs and $c$ is the hypotenuse

step 2

We know the length of one leg $a = 5$ units (half the base of the pyramid) and the hypotenuse $c = 8$ units (the slant height of the pyramid)

step 3

We need to find the length of the other leg $h$, which represents the vertical height of the pyramid

step 4

Substitute the known values into the Pythagorean theorem: $5^2 + h^2 = 8^2$

step 5

Solve for $h^2$: $h^2 = 8^2 - 5^2$

step 6

Calculate $h^2$: $h^2 = 64 - 25$

step 7

Simplify $h^2$: $h^2 = 39$

step 8

Take the square root of both sides to find $h$: $h = \sqrt{39}$

step 9

Calculate $h$: $h \approx 6.2$ units when rounded to the nearest tenth

Answer

The height is $6.2$ units.

Key Concept

Pythagorean Theorem

Explanation

The vertical height of the pyramid is found by using the Pythagorean theorem on the right triangle formed by the height, half the base, and the slant height of the pyramid.

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