Leather

Geometry Level 3

I have 150 x 180 meters of quality leather.

I want to make 5 pieces of each shapes from the leather as follows.

Square with length of 10m.

Rectangle with length of 25m and width of 40m.

Triangle with base size of 50m and height of 30m.

Circle with radius of 20m.

Trapezium with base size of 20 and 30 meters with height of 15m.

Parallelogram with base size of 18m and height of 25m.

Rhombus with diagonals of 26m and of 45m.

And a hexagon with base size of 13.5m.

Find how many percentage of leather I have to left over after cutting.

#Misc

5.44% 7.60% 6.21% 9.87%

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1 solution

Aaditya Bhatt
Jul 15, 2014

First find total area of leather.

Total area which I have is 150 x 180 = 27,000m.

Now find area of all the shapes as per information given.

Area of square = a 2 { a }^{ 2 } = 10 2 { 10 }^{ 2 } = 100m.

Area of rectangle = w * l = 25 * 40 = 1000m.

Are of triangle = b h 2 \frac { b*h }{ 2 } = 50 30 2 \frac { 50*30 }{ 2 } = 750m.

Area of circle = π r 2 \pi r^{ 2 } = π 2 0 2 \pi 20^{ 2 } = 1256m.

Area of trapezium = ( a + b 2 ) h \left( \frac { a+b }{ 2 } \right) *h = ( 20 + 30 2 ) 15 \left( \frac { 20+30 }{ 2 } \right) *15 = 375m.

Area of parallelogram = b * h = 18 * 25 = 450m.

Area of rhombus = v h 2 \frac { v*h }{ 2 } = 26 45 2 \frac { 26*45 }{ 2 } = 585m.

And area of hexagon = 3 3 2 a 2 3\frac { \sqrt { 3 } }{ 2 } { a }^{ 2 } = 3 3 2 13.5 2 3\frac { \sqrt { 3 } }{ 2 } { 13.5 }^{ 2 } = 473.50m.

Total of all shapes = 100 + 1000 + 750 + 1256 + 375 + 450 + 585 + 473.50 = 4989.50m.

We require 5 pieces of each. So 4989.50 * 5 = 24,947.50m of leather we will use.

So left over leather = 2052.50m (27,000-24947.50)

Hence leftover percentage will be 7.60% (2052.50/27,000)

More of a calculation problem than a geometry problem. Please change the side length to 13.5 in question also otherwise this ques would be reported soon for inaccuracy. @Aaditya

Krishna Ar - 6 years, 10 months ago

Area of Rhombus is ' v h ' only and not ' v h/2 ' . So the solution and indirectly question is incorrect according to me . Please recheck .

Hitarth Shah - 6 years, 10 months ago

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http://m.wikihow.com/Calculate-the-Area-of-a-Rhombus

Aaditya Bhatt - 6 years, 10 months ago

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http://m.wikihow.com/Calculate-the-Area-of-a-Rhombus U mentioned the vertical height and horizontal , so its 'v h' . If it were for diagonals then 'v h/2' .

Hitarth Shah - 6 years, 10 months ago

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@Hitarth Shah I meant to say diagonals only not base length and height. Although I corrected the question. Thanx.

Aaditya Bhatt - 6 years, 10 months ago

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@Aaditya Bhatt Okays ! U r welcome man ! ...

Hitarth Shah - 6 years, 10 months ago

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