Science & Mathematics » Mathematics » Whats the area of a rectangular polygon with one diagonal equal to 10 " and the other diagonal equal?

# Whats the area of a rectangular polygon with one diagonal equal to 10 " and the other diagonal equal?

whats the area of a rectangular poligon with one diagonal equal to 10 " and the other diagonal equal to 10"?

• rectangular polygon? not sure what that is....

regular?

if so it means the sides are 10/root2

so 100/2=50

area of 50. (its a square)
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• area=1/2 d1*d2
= 1/2(10)(10)
=50 square inches
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• Rectangular polygon with equal diagonals means that it is symmetric, so you need to find the lengths of 2 sides.
Rectangular also implies right angles at the corners.

A 10" diagonal can be extrapolated as part of a 3-4-5 right triangle - as it is the hypotenuse and a factor of 5. Apply the same factor to the other two dimensions (3 and 4), and we have sides of length 6 and 8 on a rectangle.

48 sq in in area.
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• At least 1 more piece of data is needed.
If all sides are equal,then 2a^2=100
a^2=50inch^2
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• Rectangular polygon??
Wouldn't it be simpler to call it a rectangle.

Anyway, all rectangles have 2 diagonals that are equal... always...every time
The length of rectangle can be found from length of two sides using Pythagorean Theorem.

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So if you have a rectangle with side lengths 6 and 8, then diagonals are:
d = √(6²+8²) = √(36+64) = √100 = 10

But if you have a rectangle with side lengths 2.8 and 9.6, then diagonals are:
d = √(2.8²+9.6²) = √(7.84+92.16) = √100 = 10

So here we have 2 rectangles with different side lengths, but with 2 diagonals with length 10
First rectangle has area = 6 * 8 = 48 sq inches
Second rectangle has area = 2.8 * 9.6 = 26.88 sq inches

So this question does not have enough information.

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Perhaps question actually asked "What is area of REGULAR rectangular polygon with diagonal = 10?"

In this case we are dealing with a square. We can calculate side length (s) using Pythagorean theorem:
s² + s² = 10²
2s² = 100
s² = 50

But area of square is s²

So area of REGULAR rectangular polygon with diagonal = 10 inches is
A = s² = 50 sq inches
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