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.
the sail (a triangle) has side lengths: 14 ft 7 in., 13 ft 4 in., 13 ft 4 in. and a height of 11 ft 2 in.
perimeter:
blank ft
blank in.
area
blank ft²

Explanation:

Step1: Convert all lengths to inches for perimeter calculation

First, convert each length from feet and inches to inches.
- \(14\) ft \(7\) in: \(14\times12 + 7 = 168 + 7 = 175\) in
- \(13\) ft \(4\) in: \(13\times12 + 4 = 156 + 4 = 160\) in (there are two sides of this length)
- \(11\) ft \(2\) in: \(11\times12 + 2 = 132 + 2 = 134\) in

Step2: Calculate the perimeter in inches

Perimeter \(P\) is the sum of all sides. So \(P = 175 + 160 + 160 + 134\) (wait, no, the sail is a triangle? Wait, looking at the diagram, the sail has three sides? Wait, maybe I misread. Wait, the labels: 14 ft 7 in, 13 ft 4 in, 13 ft 4 in, and 11 ft 2 in? Wait, no, maybe it's a triangle with base and two equal sides? Wait, no, the diagram shows a sail (triangle) with sides: 14 ft 7 in, 13 ft 4 in, 13 ft 4 in, and height 11 ft 2 in? Wait, no, perimeter is sum of all sides of the triangle. Wait, maybe the sail is a triangle with three sides: 14 ft 7 in, 13 ft 4 in, 13 ft 4 in. Wait, let's re - check.

Wait, the problem says "two - dimensional model" and the sail is a triangle. So perimeter is the sum of the three sides.

So sides: \(14\) ft \(7\) in, \(13\) ft \(4\) in, \(13\) ft \(4\) in.

First, convert each to feet:

- \(14\) ft \(7\) in \(= 14+\frac{7}{12}\approx14.583\) ft
- \(13\) ft \(4\) in \(= 13+\frac{4}{12}=13+\frac{1}{3}\approx13.333\) ft (two sides)

Perimeter in feet: \(14.583+13.333 + 13.333=14.583 + 26.666 = 41.249\) ft. To convert to feet and inches: \(0.249\times12\approx3\) in. So perimeter is \(41\) ft \(3\) in (approx). But let's do it in inches:

\(14\) ft \(7\) in \(=14\times12 + 7 = 175\) in

\(13\) ft \(4\) in \(=13\times12+4 = 160\) in (two sides)

So perimeter in inches: \(175+160 + 160=175 + 320 = 495\) in. Convert back to feet: \(495\div12 = 41\) ft \(3\) in (since \(41\times12 = 492\), \(495 - 492 = 3\) in).

Step3: Calculate the area

The area of a triangle is \(A=\frac{1}{2}\times base\times height\). Let's take the base as \(14\) ft \(7\) in \(=14+\frac{7}{12}=\frac{168 + 7}{12}=\frac{175}{12}\) ft, and the height as \(11\) ft \(2\) in \(=11+\frac{2}{12}=11+\frac{1}{6}=\frac{66 + 1}{6}=\frac{67}{6}\) ft.

First, convert base and height to feet:

Base \(b = 14\) ft \(7\) in \(=\frac{175}{12}\) ft \(\approx14.583\) ft

Height \(h = 11\) ft \(2\) in \(=\frac{67}{6}\) ft \(\approx11.167\) ft

Then \(A=\frac{1}{2}\times b\times h=\frac{1}{2}\times\frac{175}{12}\times\frac{67}{6}=\frac{175\times67}{144}=\frac{11725}{144}\approx81.4\) \(ft^{2}\)

Wait, let's do it in inches for more accuracy.

Base \(b = 175\) in, height \(h = 134\) in (since \(11\) ft \(2\) in \(= 134\) in)

\(A=\frac{1}{2}\times175\times134=\frac{175\times134}{2}=175\times67 = 11725\) \(in^{2}\)

Convert \(in^{2}\) to \(ft^{2}\): since \(1\) \(ft^{2}=144\) \(in^{2}\), so \(A=\frac{11725}{144}\approx81.4\) \(ft^{2}\)

Wait, let's re - calculate the perimeter correctly. The three sides of the triangle: \(14\) ft \(7\) in, \(13\) ft \(4\) in, \(13\) ft \(4\) in.

Convert each to feet:

- \(14\) ft \(7\) in \(=14+\frac{7}{12}=\frac{168 + 7}{12}=\frac{175}{12}\approx14.583\) ft
- \(13\) ft \(4\) in \(=13+\frac{4}{12}=13+\frac{1}{3}=\frac{40}{3}\approx13.333\) ft (two sides)

Perimeter \(P=\frac{175}{12}+\frac{40}{3}+\frac{40}{3}=\frac{175}{12}+\frac{160}{12}=\frac{335}{12}\approx27.9167\) ft? Wait, no, that can't be. Wait, I think I made a mistake in the number of sides. Wait, the sail: maybe the diagram has a triangle with sides: 14 ft 7 in (one side), 13 ft 4 in (another side), 13 ft 4 in (third side)? No, that would be an isoceles triangle with two equal sides of 13 ft 4 in and one side of 14 ft 7 in, and height 11 ft 2 in.

So perimeter: \(14\) ft \(7\) in \(+13\) ft \(4\) in \(+13\) ft \(4\) in

First, add the feet: \(14 + 13+13 = 40\) ft

Add the inches: \(7 + 4+4 = 15\) in \(= 1\) ft \(3\) in

So total perimeter: \(40 + 1=41\) ft \(3\) in, which is \(41\) ft \(3\) in or \(41.25\) ft.

For the area:

Base \(b = 14\) ft \(7\) in \(=14.583\) ft, height \(h = 11\) ft \(2\) in \(=11.167\) ft

\(A=\frac{1}{2}\times14.583\times11.167\approx\frac{1}{2}\times162.8\approx81.4\) \(ft^{2}\)

Answer:

Perimeter: \(41\) ft \(3\) in (or \(495\) in or \(41.25\) ft)

Area: \(\approx81.4\) \(ft^{2}\)