Q4. 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: Q4. (page 485)

Copy and complete the table below for the regular square pyramid.
$\begin{matrix} Height, 鈥� h \\ 厂濒补苍迟鈥夆赌塇别颈驳丑迟, 鈥� l & 12 \\ 叠补蝉别鈥夆赌塭诲驳别 \\ 尝补迟别谤补濒鈥夆赌塭诲驳别 & 15 \end{matrix}$

Short Answer

Expert verified

$\begin{matrix} Height, 鈥� h & 3 \sqrt{7} \\ 厂濒补苍迟鈥夆赌塇别颈驳丑迟, 鈥� l & 12 \\ 叠补蝉别鈥夆赌塭诲驳别 & 18 \\ 尝补迟别谤补濒鈥夆赌塭诲驳别 & 15 \end{matrix}$

Step by step solution

Step 1. Given information.

The slant height and lateral edge of a regular square pyramid are 12 and 15 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.

$\begin{matrix} Lateraledge = \sqrt{{(l)}^{2} + {(\frac{baseedge}{2})}^{2}} \\ 15 = \sqrt{{(12)}^{2} + {(\frac{baseedge}{2})}^{2}} [substitute] \\ 225 = 144 + {(\frac{baseedge}{2})}^{2} [square] \end{matrix}$

So,

$\begin{matrix} {(\frac{baseedge}{2})}^{2} = 81 [subtract] \\ \frac{baseedge}{2} = 9 鈥奫蝉辩补耻谤别谤辞辞迟闭 \\ baseedge = 18 [multiply] \end{matrix}$

And

$\begin{matrix} Baseedge = 2 \sqrt{{(l)}^{2} 鈭� {(h)}^{2}} \\ 18 = 2 \sqrt{{(12)}^{2} 鈭� {(h)}^{2}} [substitute] \\ 9 = \sqrt{144 鈭� h^{2}} [squareanddivide] \end{matrix}$

So, the height is:

$\begin{matrix} 144 鈭� h^{2} = 81 [square] \\ h = 3 \sqrt{7} [simplify] \end{matrix}$

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91影视

Copy and complete the table below for the regular square pyramid.
$\begin{matrix} Height, 鈥� h \\ 厂濒补苍迟鈥夆赌塇别颈驳丑迟, 鈥� l & 12 \\ 叠补蝉别鈥夆赌塭诲驳别 \\ 尝补迟别谤补濒鈥夆赌塭诲驳别 & 15 \end{matrix}$

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�h厂濒补苍迟鈥夆赌塇别颈驳丑迟,鈥�l12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15

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

Geometry

Pure Maths

Statistics

Probability and Statistics

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Copy and complete the table below for the regular square pyramid.
$\begin{matrix} Height, 鈥� h \\ 厂濒补苍迟鈥夆赌塇别颈驳丑迟, 鈥� l & 12 \\ 叠补蝉别鈥夆赌塭诲驳别 \\ 尝补迟别谤补濒鈥夆赌塭诲驳别 & 15 \end{matrix}$