Plane Geometry

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PSAT Math › Plane Geometry

Questions 1 - 10

1

What is the area of a square that has a diagonal whose endpoints in the coordinate plane are located at (-8, 6) and (2, -4)?

100

100√2

50√2

50

200√2

Explanation

Square_part1

Square_part2

Square_part3

2

A regular seven sided polygon has a side length of 14”. What is the measurement of one of the interior angles of the polygon?

128.57 degrees

257.14 degrees

180 degrees

154.28 degrees

252 degrees

Explanation

The formula for of interior angles based on a polygon with a number of side n is:

Each Interior Angle = (n-2)*180/n

= (7-2)*180/7 = 128.57 degrees

3

Hexagon

Note: Figure NOT drawn to scale.

Refer to the above figure. Evaluate .

Explanation

The sum of the degree measures of the angles of a (six-sided) hexagon, is

$180 ^{\circ } \times (6 - 2) = 180 ^{\circ } \times 4 = 720^{\circ }$

We can solve for in the equation

4

Three angles of a hexagon measure $65^{\circ}, 74^{\circ}, 89^{\circ}$ . The other three angles are congruent to one another. What is the measure of each of the latter three angles?

$164^{\circ}$

This hexagon cannot exist.

$174^{\circ}$

$48^{\circ}$

$58^{\circ}$

Explanation

The sum of the degree measures of the angles of a (six-sided) hexagon, is

$180 ^{\circ } \times (6 - 2) = 180 ^{\circ } \times 4 = 720^{\circ }$

Let be the common measure of the three congruent angles in question. We can solve for in the equation

5

Hexagon

Note:Figure NOT drawn to scale.

Refer to the above figure. Evaluate .

Explanation

The sum of the degree measures of the angles of a (six-sided) hexagon, is

$180 ^{\circ } \times (6 - 2) = 180 ^{\circ } \times 4 = 720^{\circ }$

We can solve for in the equation

6

Hexagon

Note: Figure NOT drawn to scale.

The perimeter of the above figure is 600. The ratio of to is . Evaluate .

Explanation

The perimeter of the figure can be expressed in terms of the variables by adding:

$A + B + A + B + \left (2A + 2B \right ) + \left (2A + 2B \right ) = P$

Simplify and set :

Since the ratio of to is equivalent to - or

$\frac{A}{B} = \frac{3}{2}$ ,

then

$A = \frac{3}{2} B$

and we can substitute as follows:

$6 \cdot \frac{3}{2}B + 6B= 600$

7

Hexagon

Note: Figure NOT drawn to scale.

The perimeter of the above figure is 132. What is ?

$16 \frac{1}{2}$

$26\frac{2}{5}$

Explanation

The perimeter of the figure can be expressed in terms of the variables by adding:

$A + B + A + B + \left (2A + 2B \right ) + \left (2A + 2B \right ) = P$

Simplify and set :

$6\left (A + B \right )= 132$

8

Hexagon

Note: Figure NOT drawn to scale.

The perimeter of the above figure is 600. The ratio of to is . Evaluate .

Explanation

The perimeter of the figure can be expressed in terms of the variables by adding:

$A + B + A + B + \left (2A + 2B \right ) + \left (2A + 2B \right ) = P$

Simplify and set :

Since the ratio of to is equivalent to - or

$\frac{A}{B} = \frac{3}{2}$ ,

then

$A = \frac{3}{2} B$

and we can substitute as follows:

$6 \cdot \frac{3}{2}B + 6B= 600$

9

Hexagon

Note:Figure NOT drawn to scale.

Refer to the above figure. Evaluate .

Explanation

The sum of the degree measures of the angles of a (six-sided) hexagon, is

$180 ^{\circ } \times (6 - 2) = 180 ^{\circ } \times 4 = 720^{\circ }$

We can solve for in the equation

10

Hexagon

Note: Figure NOT drawn to scale.

Refer to the above figure. Evaluate .

Explanation

The sum of the degree measures of the angles of a (six-sided) hexagon, is

$180 ^{\circ } \times (6 - 2) = 180 ^{\circ } \times 4 = 720^{\circ }$

We can solve for in the equation

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