Chapter 12: Q6. (page 485)

Copy and complete the table below for the regular square pyramid.
$\begin{matrix} Height, h & 6 \\ Slant Height, l \\ Base edge \\ Lateral edge & 10 \end{matrix}$

Short Answer

Expert verified

$\begin{matrix} Height, h & 6 \\ Slant Height, l & 2 \sqrt{17} \\ Base edge & 8 \sqrt{2} \\ Lateral edge & 10 \end{matrix}$

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:

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

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.

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

So, the slant height is:

$\begin{matrix} 2 l^{2} = 136 [add] \\ l^{2} = 68 [divide] \\ l = 2 \sqrt{17} [simplify] \end{matrix}$

And

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

Then,

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

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Copy and complete the table below for the regular square pyramid.
$\begin{matrix} Height, h & 6 \\ Slant Height, l \\ Base edge \\ Lateral edge & 10 \end{matrix}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Determine the values.

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Copy and complete the table below for the regular square pyramid.Height, h6Slant Height, lBase edgeLateral edge10

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

Applied Mathematics

Calculus

Pure Maths

Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Copy and complete the table below for the regular square pyramid.
$\begin{matrix} Height, h & 6 \\ Slant Height, l \\ Base edge \\ Lateral edge & 10 \end{matrix}$