Chapter 11.5, Problem 14PPS

To determine

To find: The approximate area of the large trivet.

Answer to Problem 14PPS

The area of the large trivet is $6.9{\text{in}}^{\text{2}}$ .

Explanation of Solution

Given:

The trivet is equilateral triangle.

The perimeter of the small trivet is of 9 inches and the large one is of 12 inches.

The area of the small trivet is of 3.9 square inches.

Calculation:

Two polygons are similar only when the corresponding angles are equal and congruent and corresponding side length are in proportion.

Consider the formula to determine the scale factor is,

  $k^2=\frac{A_1}{A_2}$

As both the figure are similar then,

  $\begin{array}{l}{\left(\frac{9\text{in}}{12\text{in}}\right)}^2=\frac{3.9}{A}\\ A={\left(\frac{12\text{in}}{9\text{in}}\right)}^{2}3.9\\ A=\frac{144\times 3.9}{81}\\ A=6.9{\text{in}}^{\text{2}}\end{array}$

Thus, the area of the large trivet is $6.9{\text{in}}^{\text{2}}$ .