How to find the length of a side of a polygon - PSAT Math

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Question

If the following shape was going to be drawn in a circle, what is the minimum radius of the circle?

Sat_math_picture3

Answer

IF you draw the longest diagonal across the shape, the length of it is 13.4. This means the radius must be at least 6.7. The answer is 7.

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Question

Heptagon

Note: Figure NOT drawn to scale.

The above polygon has perimeter 190. Evaluate .

Answer

To get the expression equivalent to the perimeter, add the lengths of the sides:

Since the perimeter is 190, we can simplify this to

and solve as follows:

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Question

Heptagon

Note: Figure NOT drawn to scale.

The perimeter of the above polygon is 225. Also, .

Evaluate .

Answer

To get the expression equivalent to the perimeter, add the lengths of the sides:

Since the perimeter is 225, we can simplify this to

and, furthermore, since ,

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