Chapter 11.1, Problem 5PSA

a

To determine

To find : The area of a square with given side

Answer to Problem 5PSA

The area is $A=144$

Explanation of Solution

Given information : The following information has been given

The length of the square $l=12$

Formula used : The area of any square will be

  $A={(length)}^2$

Calculation : We know that the area of any square will be

  $A={(length)}^2$

Hence, substituting the values from the given information, we get

  $A={(12)}^2=144$

Thus, we get

  $A=144$

b

To determine

To find : The area of a square with given diagonal

Answer to Problem 5PSA

The area is $A=50$

Explanation of Solution

Given information : The following information has been given

The diagonal of the square $d=10$

Formula used : The area of any square will be

  $A={(length)}^2$

Calculation : we calculate the length of the square from the diagonal as

  $a=\frac{d}{\sqrt{2}}=\frac{10}{\sqrt{2}}$

We know that the area of any square will be

  $A={(length)}^2$

Hence, substituting the values from the given information, we get

  $A={\left[\frac{10}{\sqrt{2}}\right]}^2=50$

Thus, we get

  $A=50$

c

To determine

To find : The side of a square with given area

Answer to Problem 5PSA

The side is $a=7$

Explanation of Solution

Given information : The following information has been given

The area of the square $A=49$

Formula used : The area of any square will be

  $A={(length)}^2$

Calculation : We know that the area of any square will be

  $A={(length)}^2$

Hence, substituting the values from the given information, we get

  $49={(a)}^2$

Thus, we get

  $a=7$

d

To determine

To find : The perimeter of a square with given area

Answer to Problem 5PSA

The perimeter is $P=36$

Explanation of Solution

Given information : The following information has been given

The area of the square $(A)=81$

Formula used : The area of any square will be

  $A={(lengt{h}_1)}^2$

Calculation : We know that the area of any square will be

  $A={(length)}^2$

Hence, substituting the values from the given information, we get

  $81={(a)}^2$

Thus, we get

  $a=9$

We know that the perimeter of any square will be

  $P=4a$

Hence, substituting the values from the given information, we get

  $P=4(9)=36$

Thus, we get

  $P=36$

e

To determine

To find : The area of a square with given perimeter

Answer to Problem 5PSA

The area is $A=81$

Explanation of Solution

Given information : The following information has been given

The perimeter of square $P=36$

Formula used : The area of any square will be

  $A={(lengt{h}_1)}^2$

Calculation : we calculate the side of the square from the perimeter as

  $P=4a=36\to a=9$

We know that the area of any square will be

  $A={(length)}^2$

Hence, substituting the values from the given information, we get

  $A={(9)}^2$

Thus, we get

  $A=81$