Question

Copy and complete the table below for the regular square pyramid.

$\begin{array}{cc}\text{Height},h& \\ \text{Slant\hspace{0.17em}\hspace{0.17em}Height},l& 5\\ \text{Base\hspace{0.17em}\hspace{0.17em}edge}& 8\\ \text{Lateral\hspace{0.17em}\hspace{0.17em}edge}& \end{array}$

Short answer

$\begin{array}{cc}\text{Height},h& 3\\ \text{Slant\hspace{0.17em}\hspace{0.17em}Height},l& 5\\ \text{Base\hspace{0.17em}\hspace{0.17em}edge}& 8\\ \text{Lateral\hspace{0.17em}\hspace{0.17em}edge}& \sqrt{41}\end{array}$

Step-by-step solution

Step 1. Given information.

The slant height and base edge of a regular square pyramid are 5 and 8 unit respectively.

Step 2. Write the concept.

The base edge is given by:

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

And the lateral edge is given by:

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

Step 3. Determine the values.

Substitute all the given values in the formula.

$\begin{array}{c}\text{Baseedge}=2\sqrt{{\left(l\right)}^2-{\left(h\right)}^2}\\ 8=2\sqrt{{\left(5\right)}^2-{\left(h\right)}^2}\text{[substitute]}\\ 4=\sqrt{25-h^2}\text{[squareanddivide]}\end{array}$

So, the height is:

$\begin{array}{c}25-h^2=16\text{[square]}\\ h=3\text{[simplify]}\end{array}$

And

$\begin{array}{c}\text{Lateraledge}=\sqrt{{\left(5\right)}^2+{\left(4\right)}^2}\text{[substitute]}\\ =\sqrt{41}\text{[simplify]}\end{array}$