Question

use a two - dimensional model and the dimensions provided to calculate the perimeter and area of the sail. round the area to the nearest tenth, if necessary. area: ft² perimeter: ft in. 14 ft 7 in. 13 ft 4 in. 11 ft 2 in. 13 ft 4 in.

Explanation:

Step1: Convert inches to feet

1 inch = 1/12 feet. So 4 inches = 4/12 = 1/3 feet and 7 inches = 7/12 feet and 2 inches=2/12 = 1/6 feet. The side - lengths of the triangle are \(a = 13+\frac{1}{3}=\frac{39 + 1}{3}=\frac{40}{3}\) feet, \(b = 14+\frac{7}{12}=\frac{168+7}{12}=\frac{175}{12}\) feet, \(c = 13+\frac{1}{3}=\frac{40}{3}\) feet, and the height \(h = 11+\frac{1}{6}=\frac{66 + 1}{6}=\frac{67}{6}\) feet.

Step2: Calculate the perimeter

The perimeter \(P=a + b + c\).
\[

$$\begin{align*} P&=\frac{40}{3}+\frac{175}{12}+\frac{40}{3}\\ &=\frac{160}{12}+\frac{175}{12}+\frac{160}{12}\\ &=\frac{160 + 175+160}{12}\\ &=\frac{495}{12}\\ & = 41.25\text{ feet} \end{align*}$$

\]

Step3: Calculate the area

The area of a triangle \(A=\frac{1}{2}\times base\times height\). Let's take the base as one of the equal - length sides. \(A=\frac{1}{2}\times\frac{40}{3}\times\frac{67}{6}\).
\[

$$\begin{align*} A&=\frac{1}{2}\times\frac{40}{3}\times\frac{67}{6}\\ &=\frac{40\times67}{36}\\ &=\frac{2680}{36}\\ &\approx74.4\text{ square feet} \end{align*}$$

\]

Answer:

Area: 74.4 square feet
Perimeter: 41.25 feet