Chapter 12: Q4. (page 485)

Copy and complete the table below for the regular square pyramid.
$\begin{matrix} Height, h \\ Slant Height, l & 12 \\ Base edge \\ Lateral edge & 15 \end{matrix}$

Short Answer

Expert verified

$\begin{matrix} Height, h & 3 \sqrt{7} \\ Slant Height, l & 12 \\ Base edge & 18 \\ Lateral edge & 15 \end{matrix}$

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:

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

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,

$\begin{matrix} {(\frac{baseedge}{2})}^{2} = 81 [subtract] \\ \frac{baseedge}{2} = 9 [sqaureroot] \\ baseedge = 18 [multiply] \end{matrix}$

And

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

So, the height is:

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

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Copy and complete the table below for the regular square pyramid.
$\begin{matrix} Height, h \\ Slant Height, l & 12 \\ Base edge \\ Lateral edge & 15 \end{matrix}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Determine the values.

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Copy and complete the table below for the regular square pyramid.Height, hSlant Height, l12Base edgeLateral edge15

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

Mechanics Maths

Discrete Mathematics

Decision Maths

Theoretical and Mathematical Physics

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Copy and complete the table below for the regular square pyramid.
$\begin{matrix} Height, h \\ Slant Height, l & 12 \\ Base edge \\ Lateral edge & 15 \end{matrix}$