Chapter 9.8, Problem 6PSA

To determine

To calculate: The slant height of a regular square pyramid.

Answer to Problem 6PSA

The slant height of a regular square pyramid is 13.

Explanation of Solution

Given information:

In a regular square pyramid,

Side $BC=10,$

Side $AF=12.$

Formula used:

The below theorem is used:

Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

  

In right angle triangle,

  $a^2+b^2\text{= }{c}^2$

Calculation:

  $\begin{array}{l}BC=10\\ FE=\frac{1}{2}(BC)\\ FE=\frac{1}{2}(10)=5\end{array}$

  

Side AE can be calculated by applying Pythagoras Theorem.

In right angle triangleAFE , we get

  $\begin{array}{l}{\left(AF\right)}^2+{\left(FE\right)}^2={\left(AE\right)}^2\\ {\left(12\right)}^2+{\left(5\right)}^2={\left(AE\right)}^2\\ 144+25={\left(AE\right)}^2\\ 169={\left(AE\right)}^2\\ \therefore AE=\sqrt{169}\\ \therefore AE=13\end{array}$