Q6. Copy and complete the table belo... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 12: Q6. (page 485)

Copy and complete the table below for the regular square pyramid.
$\begin{matrix} Height, 鈥� h & 6 \\ 厂濒补苍迟鈥夆赌塇别颈驳丑迟, 鈥� l \\ 叠补蝉别鈥夆赌塭诲驳别 \\ 尝补迟别谤补濒鈥夆赌塭诲驳别 & 10 \end{matrix}$

Short Answer

Expert verified

$\begin{matrix} Height, 鈥� h & 6 \\ 厂濒补苍迟鈥夆赌塇别颈驳丑迟, 鈥� l & 2 \sqrt{17} \\ 叠补蝉别鈥夆赌塭诲驳别 & 8 \sqrt{2} \\ 尝补迟别谤补濒鈥夆赌塭诲驳别 & 10 \end{matrix}$

Step by step solution

Step 1. Given information.

The height and lateral edge of a regular square pyramid are 6 and 10 unit respectively.

Step 2. Write the concept.

The base edge is given by:

$Baseedge = 2 \sqrt{{(l)}^{2} 鈭� {(h)}^{2}}$

And the lateral edge is given by:

$lateraledge = \sqrt{{(l)}^{2} + {(\frac{baseedge}{2})}^{2}}$

Step 3. Determine the values.

Substitute all the given values in the formula.

$\begin{matrix} Lateraledge = \sqrt{{(l)}^{2} + {(\frac{baseedge}{2})}^{2}} \\ 10 = \sqrt{{(l)}^{2} + {(\sqrt{{(l)}^{2} 鈭� {(6)}^{2}})}^{2}} [substitute] \\ 100 = l^{2} + l^{2} 鈭� 36 [square] \end{matrix}$

So, the slant height is:

$\begin{matrix} 2 l^{2} = 136 [add] \\ l^{2} = 68 鈥奫诲颈惫颈诲别闭 \\ l = 2 \sqrt{17} [simplify] \end{matrix}$

And

$\begin{matrix} Baseedge = 2 \sqrt{{(l)}^{2} 鈭� {(h)}^{2}} \\ = 2 \sqrt{{(2 \sqrt{17})}^{2} 鈭� {(6)}^{2}} [substitute] \\ = 2 \sqrt{68 鈭� 36} [square] \end{matrix}$

Then,

$\begin{matrix} Baseedge = 2 \sqrt{32} [subtract] \\ = 8 \sqrt{2} [simplify] \end{matrix}$

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91影视

Copy and complete the table below for the regular square pyramid.
$\begin{matrix} Height, 鈥� h & 6 \\ 厂濒补苍迟鈥夆赌塇别颈驳丑迟, 鈥� l \\ 叠补蝉别鈥夆赌塭诲驳别 \\ 尝补迟别谤补濒鈥夆赌塭诲驳别 & 10 \end{matrix}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Determine the values.

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91影视

Copy and complete the table below for the regular square pyramid.Height,鈥�h6厂濒补苍迟鈥夆赌塇别颈驳丑迟,鈥�l叠补蝉别鈥夆赌塭诲驳别尝补迟别谤补濒鈥夆赌塭诲驳别10

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Determine the values.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Logic and Functions

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

Copy and complete the table below for the regular square pyramid.
$\begin{matrix} Height, 鈥� h & 6 \\ 厂濒补苍迟鈥夆赌塇别颈驳丑迟, 鈥� l \\ 叠补蝉别鈥夆赌塭诲驳别 \\ 尝补迟别谤补濒鈥夆赌塭诲驳别 & 10 \end{matrix}$