In a parallelogram, the two diagonals bisect each other at their centers. Therefore, . To find , we set them equal to one another and solve. 

Plugging this value back into both equations, then adding those values together, gives us our answer of . 

When attempting to solve how many pieces of a particular object you need to cover a certain area, always make sure that your units of measurement (for the object and for the area you are covering) are the same. In the case of this question, the units of measurement are different, so you must first convert all measurements to use the same unit.

Since the tiles being used to cover the area are measured in inches, convert all units given to inches:

Length:  feet   inches

Width:  feet   inches

Then, find the area of the entire space you are covering. Since the space is rectangular (this can be assumed since only length and width are given as measurements), multiply the length and width to find the total area:  square inches.

Next, find the area of each of the tiles:  square inches. Divide the total area of the space by the area of each of your tiles: . In cases where you are covering a certain area with an object, always round up if you have a decimal (no matter how small), because you cannot simply buy  of a tile.

The answer is .

When solving such problems, always make sure that your units of measurement are all the same. In the case of this problem, you must convert feet to inches. Multiply 30 by 12 in order to get its equivalent in inches.

We know that the 30 feet corresponds with the side of the drawing that is 18 inches because it is stated that the longest side will be 30 feet. Divide 360 by 18 in order to find the ratio of the actual size of the room to the measurements on the drawing

This means that the actual measurements of the room are 20 times the measurements of the drawing. Multiply 20 times 12 in order to find the measurement of the shorter side in inches.

Divide both the 360 and 240 by 12 to convert the measurements back into feet.

Then multiply the results to get the final answer.

Use the formula for area of a trapezoid:

Where  is the area,  and  are the lengths of the two bases, and  is the height.

In this case:

Use the formula for area of a parallelogram:

Where  is the area,  is the base length, and  is the height.

In this case:

Write the formula to solve the area of a rectangle.

Substitute the dimension and area to solve for the length.

The square has 4 equal sides.  Let's assume a side is .

Each side of the square has a length of .

The area of the square is:

Substitute  into the area to solve for .

Since one side of the square is , substitute the value of   to determine the length of the square side.

The area of a square is:

Substitute the area and solve for the side.

The quantity inside the square root may not be factorized in attempt to eliminate the square root!

The side length of the square is:

By definition, a rhombus is a quadrilateral with four equal sides whose angles do not all equal 90 degrees. To find the perimeter, we must find the values of x and y. In order to do so, we must set up a system of equations where we set two sides equal to each other. Any two sides can be used to create these systems.

Here is one example:

Eq. 1

Eq. 2

Now we plug  into the first equation to find the value of :

Plugging these values into any of the three equations will give us the length of one side equaling 11.

Since there are four sides, .

A rectangle has two sets of parallel sides with all angles equaling 90 degrees. 

Since  bisects  into two equal parts, this creates an isosceles triangle .

Therefore . The sum of the angles in a triangle is 180 degrees.

Therefore