Chapter 11.5, Problem 13PSB

a.

To determine

To calculate: Length of one side and apothem of the square.

Answer to Problem 13PSB

The length of one side and apothem of the square are $11$ and $5.5$

Explanation of Solution

Given:

Area of the square is $121$

Concept used:

Here, we are using the formula

Area of the square = $a^2$ (here “ a ” is side) and Apothem = $\frac{1}{2}\times side$

Calculation:

Here, Area of the square = $a^2$

  $121=a^2$

  $a=11$

And, Apothem = $\frac{1}{2}\times side$

  → $\frac{1}{2}\times 11$

  → $5.5$

Conclusion: Hence, the length of one side and apothem of the square are $11$ and $5.5$

b.

To determine

To calculate: Length of one side and apothem of an equilateral triangle.

Answer to Problem 13PSB

The length of one side and apothem of an equilateral triangle are $12$ and $2\sqrt{3}$

Explanation of Solution

Given: Area of an equilateral triangle is $36\sqrt{3}$ sq.m

Formula used: Here, the formula is

Apothem = $\frac{\frac{s}{2}\sqrt{3}}{3}$ (here, “ s ” is side)

Area of an equilateral triangle = $\frac{\sqrt{3}}{4}{a}^2$ (here, “ a ” is side)

Calculation: Area = $\frac{\sqrt{3}}{4}{a}^2$

  $36\sqrt{3}=\frac{\sqrt{3}}{4}{a}^2$

  $a=12$

Now, Apothem = $\frac{\frac{s}{2}\sqrt{3}}{3}$

  → $\frac{\frac{12}{2}\sqrt{3}}{3}$

  → $2\sqrt{3}$

Conclusion: Hence, the length of one side and apothem of an equilateral triangle are $12$ and $2\sqrt{3}$

c.

To determine

To calculate:Length of one side and apothem of a regular hexagon.

Answer to Problem 13PSB

The length of one side and apothem of a regular hexagon are $4$ and $2\sqrt{3}$

Explanation of Solution

Given:

Perimeter of the regular hexagon is $24$ cm

Formula used: Here, the formula is

Side = $\frac{P}{n}$ (“ P ” is perimeter and “ n ” is number of sides) and Apothem = $\frac{s\sqrt{3}}{2}$

Calculation: Here, Side = $\frac{P}{n}$

  → $\frac{24}{6}=4$

Now, Apothem = $\frac{s\sqrt{3}}{2}$

  → $\frac{4\sqrt{3}}{2}$

  → $2\sqrt{3}$

Conclusion: Hence, the length of one side and apothem of a regular hexagon are $4$ and $2\sqrt{3}$