GED Math : Area of a Quadrilateral

Example Questions

Example Question #41 : Area Of A Quadrilateral

Find the area of a square with a side of .

Explanation:

Write the formula for the area of a square.

Substitute the side.

Example Question #42 : Area Of A Quadrilateral

Find the area of a square if the side length is .

Explanation:

The area of a square is:

Substitute the side into the area formula of the square.

The area is:

Example Question #43 : Area Of A Quadrilateral

A rectangle has a diagonal of  and a length of . What is the area of the rectangle?

Explanation:

The rectangle given in the question can be drawn out as thus:

Notice that the diagonal is also the hypotenuse of a right triangle that has the length and width of the rectangle as its legs. Thus, use the Pythagorean Theorem to find the length of the width of the rectangle.

Next, recall how to find the area of a rectangle.

Plug in the length and width of the rectangle.

Example Question #44 : Area Of A Quadrilateral

Suppose you receive a square sheet of wood which you are planning on making into a box. If the sheet is , find the perimeter of the sheet.

Explanation:

Suppose you receive a square sheet of wood which you are planning on making into a box. If the sheet is , find the perimeter of the sheet.

To find the perimeter of a rectangle, use the following formula:

So, let's plug in our length and width and solve:

Example Question #45 : Area Of A Quadrilateral

A rectangular television has a diagonal of  inches and a width of  inches. What is the area of the television?

Explanation:

The figure above represents the television.

Use the Pythagorean Theorem to find the length of the rectangle.

Next, recall how to find the area of a rectangle.

For the given rectangle,

Make sure to round to two places after the decimal.

Example Question #46 : Area Of A Quadrilateral

Teresa has a circular lot that has a diameter of  feet. She wants to put in a square swimming pool. In square feet, what is the largest possible area that her swimming pool can be?

Explanation:

In order to maximize the size of the swimming pool, the circular lot and the square pool must share the same center as shown by the figure below:

Now, notice that the diameter of the swimming pool is also the diagonal of the square.

We can then use the Pythagorean Theorem to find the length of a side of the square.

Solve for the side length.

Now, recall how to find the area of a square:

Plug in the found length of the side to find the area.

Example Question #47 : Area Of A Quadrilateral

Square 1 has area 16; Square 2 has perimeter 16.

Which square has the longest sides?

Square 2

Neither

The information is insufficient.

Square 1

Neither

Explanation:

The length of a side of a square is equal to the square root of its area. Square 1 has area 16, so each side has length .

The length of a side of a square is one fourth its perimeter. Square 2 has perimeter 16, so each side has length .

The squares are of equal size, so the correct response is "neither".

Example Question #48 : Area Of A Quadrilateral

Your mother made a casserole in a pan whose length is 9 inches and whose width is one and a half times the length. What is the area of the casserole pan?

Explanation:

To find the area, you need to multiply the dimensions. First, however, we need to find our width.

We can find our width by using the clue: "...one and a half times the length"

So, do the following:

Next, perform the following operation:

Example Question #49 : Area Of A Quadrilateral

In the figure below, if the minor arc  is , in degrees, what is the angle measurement of the central angle that intercepts it?

Explanation:

Recall the relationship between a central angle and the length of the arc that it intercepts.

Since the radius of the circle is given, we can find its circumference.

For the given circle,

We can plug in all the given information and solve for the central angle then.

Example Question #50 : Area Of A Quadrilateral

If a rectangular television has a diagonal of  inches and a length of  inches, what is the area of the television in square inches?