Sam F.
asked • 10/08/15Area of parallelogram
The area of a parallelogram shaped plot of land is 1600 m^2. For sale, the plot is divided into 20 equal parts- each being of the shape of a parallelogram with altitude 4 m. Find the total length of the original plot of land.
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2 Answers By Expert Tutors
Inactive Tutor answered • 10/08/15
Tutor
New to Wyzant
If each of the 20 plots had an altitude of 4m., the large parallelogram had an altitude of 80m. (20 · 4)
A = length · width
1600 m2 = length · 80m
20m = length
Inactive Tutor answered • 10/08/15
Tutor
New to Wyzant
Hi Sam, First find the area of each parallelogram.
A = 20x
1600 = 20x
80m2 = area of each small parallelogram
A = bh
80 = 4b
20m = b, base of each small parallelogram
20(5)m = total length of the original plot of land.
Inactive Tutor
Since the altitude of each small plot is 4m, they must be "stacked" horizontally. The length of each small plot, and the large plot, is 20m.
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10/08/15
Inactive Tutor
The area of a parallelogram shaped plot of land is 1600 m^2. For sale, the plot is divided into 20 equal parts- each being of the shape of a parallelogram with altitude 4 m. Find the total length of the original plot of land.
The problem states that the total Area = 1600 m^2. With 20 equal-size parts, each part has an area of 80 m^2.
We must determine the length of the original area, but the height of the original area cannot be determined because we do now know how the division was done. It could be 20*1, 4*5, ... (in neat rows and columns) or some other way of packing small parallelograms into a large parallelogram.
"Stacked horizontally" is one way to get a length measurement of 20m. A 4*5 arrangement gets (4)(4)=16 height and a (5)(20)=100m length, and so on ...
Just for humor: a 4m*20m "plot" is roughly enough space to park a 12'x60' trailer (too close to neighbors to open the door).
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10/08/15
Inactive Tutor
The problem states: "shape of a parallelogram with altitude 4 m."
The only possible dimension for the small plot is 20m x 4m.
Two possible arrangements are: 20 small plot placed end to end making a large plot 400m x 4m, or 20 small plots stacked horizontally making a large plot of 80m x 20m.
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10/08/15
Sam F.
where did the 5 came from?
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10/09/15
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10/10/15