Chapter 11.5, Problem 6PSA

a.

To determine

To calculate:Thearea of square with side XC as $5$ .

Answer to Problem 6PSA

Thearea of square is $100$ .

Explanation of Solution

Given information:

SideXC =5.

Formula used:

Perimeter of square: $P=4\times side$

  $Areaofsquare=\frac{1}{2}\times a\times P$

  $\begin{array}{l}a=Apothem,\\ P=Perimeter.\end{array}$

Calculation:

  

ΔXCB is a ${45}^{\circ }{45}^{\circ }{90}^{\circ }\Delta$ .

XC =5, so BC =5.

  $BD=2\times BC=2\times 5=10$

Perimeter is sum of all sides.

  $\begin{array}{l}P=4\times side\\ P=4\times BD\\ P=4\times 10\\ P=40\end{array}$

  $\begin{array}{l}Areaofsquare=\frac{1}{2}\times a\times P\\ =\frac{1}{2}\times 5\times 40\\ =100\end{array}$

b.

To determine

To find:The area of square with side XC as $12$ .

Answer to Problem 6PSA

The area of square is $576$ .

Explanation of Solution

Given information:

Side XC = 12.

Formula used:

Perimeter of square: $P=4\times side$

  $Areaofsquare=\frac{1}{2}\times a\times P$

  $\begin{array}{l}a=Apothem,\\ P=Perimeter.\end{array}$

Calculation:

  

ΔXCB is a ${45}^{\circ }{45}^{\circ }{90}^{\circ }\Delta$ .

XC =12, so BC =12.

  $BD=2\times BC=2\times 12=24$

Perimeter is sum of all sides.

  $\begin{array}{l}P=4\times side\\ P=4\times BD\\ P=4\times 24\\ P=96\end{array}$

  $\begin{array}{l}Areaofsquare=\frac{1}{2}\times a\times P\\ =\frac{1}{2}\times 12\times 96\\ =576\end{array}$

c.

To determine

To calculate: The area of square whose side is $7$ .

Answer to Problem 6PSA

The area of square is $49$ .

Explanation of Solution

Given information:

Side=7.

Formula used:

  $Areaofsquare=s^2$

  $s=Sideofsquare.$

Calculation:

In square, all sides are equal.

  $\begin{array}{l}A=s^2\\ A=7^2=49\end{array}$

d.

To determine

To calculate: The area of square whose diagonal is $10$ .

Answer to Problem 6PSA

The area of square is $50$ .

Explanation of Solution

Given information:

Diagonal=10.

Formula used:

  $Areaofsquare=\frac{1}{2}\times (d_1\times d_2)$

where $d=$ diagonal of square

Calculation:

In a square, the diagonals are congruent.

  $\begin{array}{l}A=\frac{1}{2}\times (d_1\times d_2)\\ A=\frac{1}{2}\times (10\times 10)\\ A=\frac{1}{2}\times (100)\\ A=50\end{array}$

e.

To determine

To find: The area of square whose radius is $6$ .

Answer to Problem 6PSA

The area of square is $72$ .

Explanation of Solution

Given information:

r =6.

Formula used:

  $Areaofsquare=\frac{1}{2}\times (d_1\times d_2)$

where $d=$ diagonal of square

Calculation:

Radius is half the diagonal. So Diagonal = 12.

In a square, the diagonals are congruent.

  $\begin{array}{l}A=\frac{1}{2}\times (d_1\times d_2)\\ A=\frac{1}{2}\times (12\times 12)\\ A=\frac{1}{2}\times (144)\\ A=72\end{array}$

f.

To determine

To calculate: The area of square whose perimeter is $12$ .

Answer to Problem 6PSA

The area of square is $9$ .

Explanation of Solution

Given information:

Perimeter=12.

Formula used:

Perimeter of square:

  $P=4\times side$

  $Areaofsquare=s^2$

where $s=sideofsquare.$

Calculation:

  $\begin{array}{l}P=4\times side\\ 12=4\times side\\ side=\frac{12}{4}=3\end{array}$

In square, all sides are equal.

  $\begin{array}{l}A=s^2\\ A=3^2=9\end{array}$