GED Math : Area of a Quadrilateral

Example Questions

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Example Question #1 : Area Of A Quadrilateral

Find the area of the trapezoid:

Explanation:

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

Example Question #45 : Squares, Rectangles, And Parallelograms

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

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 #46 : Squares, Rectangles, And Parallelograms

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?

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 #47 : Squares, Rectangles, And Parallelograms

Note: Figure NOT drawn to scale

What percent of Rectangle  is white?

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

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 #49 : Squares, Rectangles, And Parallelograms

Note: Figure NOT drawn to scale.

Calculate the area of Rhombus  in the above diagram if:

Explanation:

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

.

Example Question #50 : 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 area of the garden?

Explanation:

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

.

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

.

The area of the garden is their product:

Example Question #2 : Area Of A Quadrilateral

Note: Figure NOT drawn to scale

Refer to the above diagram.

Half of Rectangle  is pink. .

Evaluate .

Explanation:

Rectangle  has length  and width , so it has area

.

The area of Rectangle  is twice that of Rectangle , or 600. Its length is

.

Its width is

.

Plug in what we know and solve for :

Example Question #52 : 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 five feet wide throughout. What is the area of that dirt path?

Explanation:

The dirt path can be seen as the region between two rectangles. The outer rectangle has length and width 100 feet and 60 feet, respectively, so its area is

square feet.

The inner rectangle has length and width  feet and  feet, respectively, so its area is

square feet.

The area of the path is the difference of the two:

square feet.

Example Question #53 : Squares, Rectangles, And Parallelograms

Note: Figure NOT drawn to scale

What percent of Rectangle  is pink?

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

.

So we want to know what percent 112 is of 240, which can be answered as follows:

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