# GED Math : Perimeter and Sides of Quadrilaterals

## Example Questions

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### Example Question #1 : Squares, Rectangles, And Parallelograms

Note:  Figure NOT drawn to scale

Refer to the above figure, which shows a rectangular garden (in green) surrounded by a dirt path (in brown) six feet wide throughout. What is the perimeter of the garden?

Explanation:

The inner rectangle, which represents the garden, has length and width  feet and  feet, respectively, so its perimeter is

feet.

### Example Question #2 : Squares, Rectangles, And Parallelograms

Which of the following can be the sidelengths of a rhombus?

Explanation:

The four sides of a rhombus have equal length, so we can eliminate three choices by demonstrating that at least two sidelengths are not equal.

:

1,000 meters is, by definition, equal to 1 kilometer, not 0.1 kilometers. Therefore,

and this choice is incorrect.

:

1 mile is, by definition, equal to 5,280 feet, not 1,760 feet. Therefore,

and this choice is incorrect.

By definition, 1 decimeter, not 0.1 decimeter, is equal to 1 meter. Therefore,

and this choice is incorrect.

:

yard is equal to  inches and, also,  feet. Therefore,

All four sides have equal length so this is the rhombus. This is the correct choice.

### Example Question #3 : Squares, Rectangles, And Parallelograms

Identify the above polygon.

Pentagon

Hexagon

Rhombus

Trapezoid

Hexagon

Explanation:

A polygon with six sides is called a hexagon.

### Example Question #1 : Squares, Rectangles, And Parallelograms

Refer to the above three figures. All parallel sides are so indicated.

Which of the figures can be called a quadrilateral?

Figure C only

Figures A, B, and C

Figures A and B only

Figures B and C only

Figures A, B, and C

Explanation:

By definition, any polygon with four sides is called a quadrilateral. All three figures fit this description.

### Example Question #1 : Perimeter And Sides Of Quadrilaterals

Refer to the above diagram. Parallel sides are so indicated.

Identify the above polygon.

Trapezoid

Hexagon

Pentagon

Parallelogram

Trapezoid

Explanation:

A four-sided figure, or quadrilateral, with one pair of parallel sides and its other sides nonparallel is called a trapezoid.

### Example Question #6 : Squares, Rectangles, And Parallelograms

Refer to the above figure. You are given that  and that  is acute.

Which of the following words accurately describes Polygon ?

Hexagon

Parallelogram

Pentagon

Trapezoid

Trapezoid

Explanation:

Polygon  has four sides and is therefore a quadrilateral. , so . Also, since  is acute and  is right, , so

The quadrilateral has one pair of parallel sides, and the other two sides are not parallel. Therefore, it is a trapezoid.

### Example Question #2 : Perimeter And Sides Of Quadrilaterals

Refer to the above three figures. All parallel sides are so indicated.

Which of the figures can be called a parallelogram?

Figures A and B only

Figures A, B, and C

Figure C only

Figure B only

Figures A and B only

Explanation:

A parallelogram, by definition, has two pairs of parallel sides. Figures A and B fit that criterion, but Figure C does not.

### Example Question #8 : Squares, Rectangles, And Parallelograms

Note:  Figure NOT drawn to scale.

Refer to the above figure, which shows a rectangular garden (in green) surrounded by a dirt path (in brown). The dirt path is  feet wide throughout. Which of the following polynomials gives the perimeter of the garden?

Explanation:

The length of the garden is  than that of the entire lot, or

.

The width of the garden is  than that of the entire lot, or

.

The perimeter is twice the sum of the two:

### Example Question #9 : Squares, Rectangles, And Parallelograms

Note: Figure NOT drawn to scale.

Quadrilateral  is a rhombus. Calculate its perimeter if:

Explanation:

The four sides of a rhombus are congruent. Also, the diagonals of a rhombus are perpendicular bisectors to each other, so the four triangles they form are right triangles. Therefore, the Pythagorean theorem can be used to determine the common sidelength of Quadrilateral .

We focus on . The diagonals of a rhombus, as is the case with any parallelogram, are each the other's bisector, so

By the Pythagorean Theorem,

13 is the common length of the four sides of Quadrilateral , so its perimeter is .

### Example Question #10 : Squares, Rectangles, And Parallelograms

Note: Figure NOT drawn to scale

Give the ratio of the perimeter of Rectangle  to that of Rectangle .

Explanation:

The perimeter of Rectangle  is

.

Opposite sides of a rectangle are congruent, so

and

.

The perimeter of Rectangle  is

.

Opposite sides of a rectangle are congruent, so

,

,

and

.

The ratio of the perimeters is

- that is, 10 to 7.

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