How to find the length of a side of a polygon

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

Questions 1 - 3

1

Heptagon

Note: Figure NOT drawn to scale.

The above polygon has perimeter 190. Evaluate .

Explanation

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:

$2\left ( A + B + C \right )+ 20 = 190$

$2\left ( A + B + C \right )= 170$

2

Heptagon

Note: Figure NOT drawn to scale.

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

Evaluate .

$B = 51\frac{1}{4}$

Insufficient information exists to answer the question.

$B = 56\frac{1}{4}$

$B = 34\frac{1}{6}$

$B = 37 \frac{1}{2}$

Explanation

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 ,

$2B +2\left (A + C \right )= 205$

$B = 51\frac{1}{4}$

3

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

Sat_math_picture3

7

8

9

10

11

Explanation

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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