GED Math : Squares, Rectangles, and Parallelograms

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

Rhombus

Hexagon

Trapezoid

Hexagon

Explanation:

A polygon with six sides is called a hexagon.

Example Question #4 : 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 B and C only

Figures A and B only

Figures A, B, and C

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 #5 : Squares, Rectangles, And Parallelograms Refer to the above diagram. Parallel sides are so indicated.

Identify the above polygon.

Parallelogram

Pentagon

Trapezoid

Hexagon

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 #7 : Squares, Rectangles, And Parallelograms 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

Figure C only

Figure B only

Figures A, B, and C

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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