A sail maker needs to stitch a sail with dimensions 5 feet by 8 feet by 10 feet. If cloth costs \$3.50

per square foot, find the cost of material to make the sail.

Relevance
• The sail area is a right tringle.

Hence

A = (1/2)5 x 8

A = 20sq.ft.

Hence cost is 20 sq.ft. X \$3.50 = \$70.00

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• Realistically, sailcloth would be sold in parallel-sided yardage.  You couldn't buy a piece of cloth the exact size and triangular shape you wanted.

Many sails I've seen have been sewn in narrow parallel strips.  You could come pretty close to the minimum amount of cloth needed using that technique.

• The fact that the question admits the need for stitching also admits the need for overlap.

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• Linear units are [ft]. Triangle sides are (a,b,c) = (5,8,10).

We shall use Heron's formula to calculate the sail area.

s = (1/2)(a+b+c) = (1/2)(23) =11.5.

Designating A as sail area we have A^2 = s(s-a)(s-b)(s-c) = (11.5)(6.5)(3.5)(1.5).

Then (2^4)A^2 = (23)(13)(7)(3) = 6279, A^2 = 392.4375 & A = 19.81[ft]^2.

At a cost of \$3.5 per square foot of sail material, the total sail material cost will be

\$(3.5)(19.81) = \$69.34.

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• apply this formula

s = 1/2(a + b + c)

A = √[s(s - a)(s - b)(s - c)]

s = 1/2(5 + 8 + 10) = 23/2 ft

A = √[23/2(23/2 - 5)(23/2 - 8)(23/2 - 10)]

A = 19.81 ft^2

cost of material = \$3.50 * 19.81ft = \$69.34 answer//

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• A sail maker needs to stitch a sail with dimensions 5 feet by 8 feet by 10 feet.

If cloth costs \$3.50 per square foot,

find the cost of material to make the sail.

Area of the sail is 19.81004 ft^2

The cost of material to make the sail is \$69.34.

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• You can use this equation to find the area of a triangle given the three lengths:

A = √[s(s - a)(s - b)(s - c)]

Where "s" is half of the perimeter:

s = (a + b + c) / 2

Given:

a = 5, b = 8, c = 10

We can find a value for "s", then substitute all four into the area equation:

s = (5 + 8 + 10) / 2

s = 23 / 2

s = 11.5

A = √[11.5(11.5 - 5)(11.5 - 8)(11.5 - 10)]

A = √[11.5(6.5)(3.5)(1.5)]

A = √392.4375

A = 19.8100 ft² (rounded to 4 DP)

Now that we have the area, at \$3.50 per ft², the total cost of materials is:

19.81 * 3.5 = \$69.34 (rounded to the nearest penny)

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• A = sqrt 392.4375  =  19.81

cost = \$69.34

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