### All ACT Math Resources

## Example Questions

### Example Question #2 : How To Find The Perimeter Of A Parallelogram

Note: Figure NOT drawn to scale.

Give the perimeter of Parallelogram in the above diagram.

**Possible Answers:**

**Correct answer:**

By the 30-60-90 Theorem, the length of the short leg of is the length of the long leg divided by , so

Its hypotenuse has twice the length of the short leg, so

The perimeter of the parallelogram is

### Example Question #3 : How To Find The Perimeter Of A Parallelogram

Note: Figure NOT drawn to scale.

Give the perimeter of Parallelogram in the above diagram.

**Possible Answers:**

**Correct answer:**

By the 45-45-90 Theorem, the lengths of the legs of are equal, so

Its hypotenuse has measure that of the common measure of its legs, so

The perimeter of the parallelogram is

### Example Question #4 : How To Find The Perimeter Of A Parallelogram

Note: Figure NOT drawn to scale.

To the nearest tenth, give the perimeter of Parallelogram in the above diagram.

**Possible Answers:**

**Correct answer:**

The perimeter of the parallelogram is

### Example Question #5 : How To Find The Perimeter Of A Parallelogram

In the above figure, Parallelogram has area 100. To the nearest tenth, what is its perimeter?

**Possible Answers:**

**Correct answer:**

By the 45-45-90 Theorem, . Since and are its base and height:

Also by the 45-45-90 Theorem,

The perimeter of the parallelogram is

### Example Question #6 : How To Find The Perimeter Of A Parallelogram

In the above figure, Parallelogram has area 100. To the nearest tenth, what is its perimeter?

**Possible Answers:**

**Correct answer:**

By the 30-60-90 Theorem,

The area of the parallelogram is the product of height and base , so

Also by the 30-60-90 Theorem,

The perimeter of the parallelogram is

### Example Question #7 : How To Find The Perimeter Of A Parallelogram

Note: Figure NOT drawn to scale.

In the above figure, Parallelogram has area 100. To the nearest tenth, what is its perimeter?

**Possible Answers:**

**Correct answer:**

The area of the parallelogram is the product of height and base , so

The perimeter of the parallelogram is

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

If a rectangular plot measures by , what is the length of the diagonal of the plot, in feet?

**Possible Answers:**

**Correct answer:**

To answer this question, we must find the diagonal of a rectangle that is by . Because a rectangle is made up of right angles, the diagonal of a rectangle creates a right triangle with two of the sides.

Because a right triangle is formed by the diagonal, we can use the Pythagorean Theorem, which is:

and each represent a different leg of the triangle and represents the length of the hypotenuse, which in this case is the same as the diagonal length.

We can then plug in our known values and solve for

We now must take the square root of each side so that we can solve for

Therefore, the diagonal of the rectangle is .

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

is a parallelogram. Find the length of diagonal .

**Possible Answers:**

**Correct answer:**

To find the length of the diagonal, we can consider only the triangle and use the law of cosines to find the length of the unknown side.

The Law of Cosines:

Where is the length of the unknown side, and are the lengths of the known sides, and is the angle between and .

From the problem:

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

is a parallelogram. Find the length of diagonal .

**Possible Answers:**

**Correct answer:**

To find the length of the diagonal, we can consider only the triangle and use the law of cosines to find the length of the unknown side.

The Law of Cosines:

Where is the length of the unknown side, and are the lengths of the known sides, and is the angle between and .

From the problem:

### Example Question #4 : How To Find The Length Of The Diagonal Of A Parallelogram

is a parallelogram. Find the length of diagonal .

**Possible Answers:**

**Correct answer:**

To find the length of the diagonal, we can consider only the triangle and use the law of cosines to find the length of the unknown side.

The Law of Cosines:

Where is the length of the unknown side, and are the lengths of the known sides, and is the angle between and .

From the problem: