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. 14 ft 7 in. 13 ft 4 in. 11 ft 2 in. 13 ft 4 in. perimeter: ft in. area: ft²

Explanation:

Step1: Convert inches to feet

1 inch = $\frac{1}{12}$ ft.
7 inches = $7\times\frac{1}{12}=\frac{7}{12}\approx0.583$ ft, so 14 ft 7 in = $14 + 0.583=14.583$ ft.
4 inches = $4\times\frac{1}{12}=\frac{1}{3}\approx0.333$ ft, so 13 ft 4 in = $13+ 0.333 = 13.333$ ft.
2 inches = $2\times\frac{1}{12}=\frac{1}{6}\approx0.167$ ft, so 11 ft 2 in = $11 + 0.167=11.167$ ft.

Step2: Calculate the perimeter

Perimeter $P$ of a triangle is the sum of its side - lengths.
$P=14.583 + 13.333+11.167+13.333$
$P = 52.416$ ft.
$0.416\times12 = 5$ in (approx). So the perimeter is 52 ft 5 in.

Step3: Use Heron's formula to calculate the area

Let $a = 14.583$, $b = 13.333$, $c = 11.167$, $d = 13.333$. First, find the semi - perimeter $s$ of the two - triangle combination (the sail).
$s=\frac{a + b + c + d}{2}=\frac{14.583+13.333+11.167+13.333}{2}=\frac{52.416}{2}=26.208$
The area $A$ using Heron's formula $A=\sqrt{(s - a)(s - b)(s - c)(s - d)}$
$A=\sqrt{(26.208 - 14.583)(26.208 - 13.333)(26.208 - 11.167)(26.208 - 13.333)}$
$A=\sqrt{11.625\times12.875\times15.041\times12.875}$
$A=\sqrt{(11.625\times15.041)\times(12.875\times12.875)}$
$A=\sqrt{174.856\times165.766}$
$A=\sqrt{29087.7}$
$A\approx170.5$ $ft^{2}$

Answer:

perimeter: 52 ft 5 in
area: 170.5 $ft^{2}$