# ACT Math : Other Quadrilaterals

## Example Questions

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### Example Question #1 : How To Find If Quadrilaterals Are Similar

The sides of rectangle A measure to , and . Rectangle B is similar to Rectangle A. The shorter sides of rectangle B measure  each. How long are the longer sides of Rectangle B?

Explanation:

In similar rectangles, the ratio of the sides must be equal.

To solve this question, the following equation must be set up:

, using  as the variable for the missing side.

We then must cross multiply, which leaves us with:

Lastly, we divide both sides by 8 to solve for the missing side:

Therefore, the longer sides of the rectangle are each .

### Example Question #2 : How To Find If Quadrilaterals Are Similar

Suppose a rectangle has side lengths of 7 and 3.  Another rectangle has another set of side lengths that are 8 and 4.  Are these similar rectangles, and why?

Explanation:

Set up the proportion to determine if the ratios of both rectangles are equal.

If they are, then they are similar.

These are not similar rectangles since their ratios are not the same.

### Example Question #1 : How To Find The Length Of The Diagonal Of A Quadrilateral

A square has a length of .  What must be the length of the diagonal?

Explanation:

A square with a length of  indicates that all sides are  since a square has 4 equal sides.  Use the Pythagorean Theorem to solve for the diagonal.

### Example Question #2 : How To Find The Length Of The Diagonal Of A Quadrilateral

If the rectangle has side lengths of  and , what is the diagonal of the rectangle?

Explanation:

Use the Pythagorean Theorem to solve for the diagonal.

### Example Question #3 : How To Find The Length Of The Diagonal Of A Quadrilateral

In the parallelogram above,  and . What is the length of the diagonal ?

Explanation:

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

### Example Question #1 : How To Find The Area Of A Quadrilateral

Jane plans to re-tile her kitchen with tiles that have a length of  inches and a width of  inches wide. If her kitchen measures  feet by  feet, how many tiles will she need?

Explanation:

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.

### Example Question #1 : How To Find The Area Of A Quadrilateral

Vikram is looking at a scale drawing of a room he is building. The drawing is of a rectangle that measures  inches by  inches. If he knows the length of the longer side of the room will measure  feet, what is the area of the room?

Explanation:

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.

### Example Question #3 : How To Find The Area Of A Quadrilateral

If a trapezoid has base lengths of  and  and a height of , what is its area?

Explanation:

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:

### Example Question #4 : How To Find The Area Of A Quadrilateral

A parallelogram has a side length of , a height of , and a base length of . What is its area?

Explanation:

Use the formula for area of a parallelogram:

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

In this case:

### Example Question #1 : Other Quadrilaterals

Find the length of a rectangle if the area is , and the width is .