Chapter 11.5, Problem 12PSB

a.

To determine

To calculate:The area of an equilateral triangle

Answer to Problem 12PSB

The area of an equilateral triangle is $\frac{81\sqrt{3}}{4}$

Explanation of Solution

Given:

The side of an equilateral triangle is $9$

Concept used:

Here, we are using the formula

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

Calculation:

Here, Area of equilateral triangle = $\frac{\sqrt{3}}{4}{a}^2$

  → $\frac{\sqrt{3}}{4}\times 81$

  → $\frac{81\sqrt{3}}{4}$

Conclusion: Hence, the area of an equilateral triangle is $\frac{81\sqrt{3}}{4}$

b.

To determine

To calculate:Area of the square.

Answer to Problem 12PSB

Area of the square is $225$

Explanation of Solution

Given:

Apothem of the square is $7\frac{1}{2}$

Formula used:

Here, the formula is

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

Calculation:

  $7.5=\frac{1}{2}\times side$

  $side=15$

So, $15\times 15=225$

Conclusion: Hence, the area of the square is $225$

c.

To determine

To calculate: Area of a regular hexagon.

Answer to Problem 12PSB

Area of a regular hexagon is $\frac{147\sqrt{3}}{2}$

Explanation of Solution

Given: Side of the regular hexagon is $7$

Formula used: Here, the formula is

Area of regular hexagon = $\frac{3\sqrt{3}}{2}\times a^2$

Calculation: Area of regular hexagon = $\frac{3\sqrt{3}}{2}\times 49$

  → $\frac{147\sqrt{3}}{2}$

Conclusion: Hence, the area of a regular hexagon is $\frac{147\sqrt{3}}{2}$