GED Math : 2-Dimensional Geometry

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #36 : Squares, Rectangles, And Parallelograms

Square 1 has area 64; Square 2 has perimeter 24.

Give the ratio of the length of a side of Square 1 to the length of a side of Square 2.

Possible Answers:

Correct answer:

Explanation:

The length of a side of a square is equal to the square root of its area. Square 1 has area 64, so each side has length .

The length of a side of a square is one fourth its perimeter. Square 2 has perimeter 24, so each side has length .

The ratio of the sidelengths is - that is, .

Example Question #331 : 2 Dimensional Geometry

A square and a right triangle share a side as shown by the figure below.

2

Find the area of the square.

Possible Answers:

Correct answer:

Explanation:

2

Notice that the side of the square is the same as the hypotenuse of the right triangle.

Use Pythagorean's theorem to find the length of the hypotenuse.

Now that we have the length of a side of the square, find the area.

Example Question #42 : Perimeter And Sides Of Quadrilaterals

2

Find the perimeter of trapezoid  if .

Possible Answers:

Correct answer:

Explanation:

2

Since we know that , we can set up the following ratio to find the lengths of  and  because of the  triangle.

Using that value,

Thus, we can find the perimeter of the trapezoid.

3

Example Question #332 : 2 Dimensional Geometry

What is the perimeter of a square that has an area of ?

Possible Answers:

Correct answer:

Explanation:

First we need to recognize that in order to find perimeter we first need to figure out the length of each side of the square. The formula for area of a square is

 

where  is side

To solve for  we need to take the square root of both sides

Now that we know our side length is 13, we can plug it into our perimeter equation and solve for s

We multiply 4 and 13

Notice our answer is in ft because perimeters are linear

Example Question #333 : 2 Dimensional Geometry

Find the area of the trapezoid:

Question_10

Possible Answers:

Correct answer:

Explanation:

The area of a trapezoid is calculated using the following equation:

Example Question #2 : Area Of A Quadrilateral

The length of each side of a square is increased by 10%. By what percent has its area increased?

Possible Answers:

Correct answer:

Explanation:

Let  be the original sidelength of the square. Increasing this by 10% is the same as adding 0.1 times that sidelength to the original sidelength. The new sidelength is therefore

The area of a square is the square of its sidelength. 

The area of the square was originally ; it is now 

That is, the area has increased by

.

Example Question #3 : Area Of A Quadrilateral

Swimming_pool

The above figure depicts the rectangular swimming pool at an apartment. The apartment manager needs to purchase a tarp that will cover this pool completely. However, because of the cutting device the pool store uses, the length and the width of the tarp must each be a multiple of four yards. Also, the tarp must be at least one yard longer and one yard wider than the pool.

What will be the minimum area of the tarp the manager purchases?

Possible Answers:

Correct answer:

Explanation:

Three feet make a yard, so the length and width of the pool are  yards and  yards, respectively. Since the dimensions of the tarp must exceed those of the pool by at least one yard, the tarp must be at least  yards by  yards; but since both dimensions must be multiples of four yards, we take the next multiple of four for each.

The tarp must be 20 yards by 16 yards, so the area of the tarp is the product of these dimensions, or

 square yards.

Example Question #4 : Area Of A Quadrilateral

Rectangle

Note: Figure NOT drawn to scale

What percent of Rectangle  is white?

Possible Answers:

Correct answer:

Explanation:

The pink region is Rectangle . Its length and width are

so its area is the product of these, or

.

The length and width of Rectangle  are

so its area is the product of these, or

.

The white region is Rectangle  cut from Rectangle , so its area is the difference of the two:

.

So we want to know what percent 102 is of 200, which can be answered as follows:

Example Question #1303 : Ged Math

Garden

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 five feet wide throughout. Which of the following polynomials gives the area of the garden in square feet?

Possible Answers:

Correct answer:

Explanation:

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

.

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

.

The area of the garden is their product:

Example Question #333 : 2 Dimensional Geometry

Rhombus

Note: Figure NOT drawn to scale.

Calculate the area of Rhombus  in the above diagram if:


Possible Answers:

Correct answer:

Explanation:

The area of a rhombus is half the product of the lengths of diagonals  and . This is

.

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