Chapter 12: Q21. (page 486)

Find the following for the regular triangular pyramid.
If AM = 9 and VA = 10, find h and l.

Short Answer

Expert verified

$h = 8 and l = \sqrt{73}$

Step by step solution

Step 1. Given information.

The figure provided in the question,

$A M = 9 and V A = 10$

Step 2. Determine l.

Since $A M = 9$ ,

$\begin{matrix} \frac{\sqrt{3}}{2} a = 9 \\ a = \frac{18}{\sqrt{3}} [multiply] \\ a = 6 \sqrt{3} [simplify] \end{matrix}$

Now, $V A = 10$ ,

$\begin{matrix} l = \sqrt{{(10)}^{2} - {(\frac{6 \sqrt{3}}{2})}^{2}} \\ = \sqrt{100 - 27} [square] \\ = \sqrt{73} [subtract] \end{matrix}$

Step 3. Determine h.

Now determine the height of pyramid.

$\begin{matrix} h^{2} + {(3)}^{2} = {(\sqrt{73})}^{2} \\ h^{2} = 73 - 9 [sqaureandsubtract] \\ h^{2} = 64 [subtract] \\ h = 8 [squareroot] \end{matrix}$

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Find the following for the regular triangular pyramid.
If AM = 9 and VA = 10, find h and l.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine l.

Step 3. Determine h.

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Find the following for the regular triangular pyramid.If AM = 9 and VA = 10, find h and l.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine l.

Step 3. Determine h.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Calculus

Mechanics Maths

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Find the following for the regular triangular pyramid.
If AM = 9 and VA = 10, find h and l.