Chapter 9.8, Problem 5PSA

a.

To determine

To calculate:Thelength of a side $AD$ .

Answer to Problem 5PSA

The length of a side $AD$ is $14$ .

Explanation of Solution

Given information:

In a regular square pyramid,

Side $ID=14,$

Side $PY=24.$

Formula used:

As base of pyramid is square, each side is equal

Calculation:

  

It is given that in a regular square pyramid,

Side $ID=14$

MIDA is a square. In a square, all sides are equal.

  $AD=ID=14$

b.

To determine

To find: The length of side $YR$ .

Answer to Problem 5PSA

The length of side $YR$ is $7.$

Explanation of Solution

Given information:

In a regular square pyramid,

Side $ID=14,$

Side $PY=24.$

Formula used:

The sideYR is half of any of the sides of the square.

Calculation:

  

As PY is perpendicular to YR and it is perpendicular at mid-point of line YR , the length of YR will be half of any side of a square.

  $YR=\frac{1}{2}(ID)=\frac{1}{2}\ast 14=7$

c.

To determine

To find: The length of side $PR$ .

Answer to Problem 5PSA

The length of side $PR$ is $25$ .

Explanation of Solution

Given information:

In a regular square pyramid,

Side $ID=14,$

Side $PY=24.$

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:

  

Side PR can be calculated by applying Pythagoras Theorem.

In right angle triangle PYR , we get

  $\begin{array}{l}{\left(PY\right)}^2+{\left(YR\right)}^2={\left(PR\right)}^2\\ {\left(24\right)}^2+{\left(7\right)}^2={\left(PR\right)}^2\\ 576+49={\left(PR\right)}^2\\ 625={\left(PR\right)}^2\\ \therefore PR=\sqrt{625}\\ \therefore PR=25\end{array}$

d.

To determine

To find: The perimeter of the base $AMID$ .

Answer to Problem 5PSA

Theperimeter of the base $AMID$ is $56$ .

Explanation of Solution

Given information:

In a regular square pyramid,

Side $ID=14,$

Side $PY=24.$

Formula used:

Perimeter = Sum of all sides.

Calculation:

  

AMIDis a square.

  $\begin{array}{l}P(AMID)=AM+MI+ID+DA\\ =14+14+14+14\\ =56\end{array}$

e.

To determine

To calculate: The length of diagonal $AI$ of a base square.

Answer to Problem 5PSA

The length of diagonal of $AI$ is $14\sqrt{2}$ .

Explanation of Solution

Given information:

In a regular square pyramid,

Side $ID=14,$

Side $PY=24.$

Formula used:

The length of diagonal of a square is $side\sqrt{2}$ .

Calculation:

  

AMIDis a square.

  $\begin{array}{l}Diagonal=side\sqrt{2}\\ AI=ID\sqrt{2}\\ AI=14\sqrt{2}\end{array}$