Quadrilaterals

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1

The perimeter of a square is 48. What is the length of its diagonal?

Explanation

Perimeter = side * 4

48 = side * 4

Side = 12

We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles.

Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

2

The perimeter of a square is 48. What is the length of its diagonal?

Explanation

Perimeter = side * 4

48 = side * 4

Side = 12

We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles.

Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

3

The perimeter of a square is 48. What is the length of its diagonal?

Explanation

Perimeter = side * 4

48 = side * 4

Side = 12

We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles.

Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

4

Find the area of the following rhombus:

Screen_shot_2014-03-01_at_8.57.04_pm

The perimeter of the rhombus is .

Explanation

The formula for the perimeter of a rhombus is:

Where is the length of the side

Plugging in our values, we get:

The formula for the area of a rhombus is:

Where is the length of one diagonal and is the length of another diagonal

By drawing the diagonals, we create a right triangle with the hypotenuse as and the side as .

Since we know that is a phythagorean triple, we can infer that the third side is .

Plugging in our values, we get:

5

Find the area of the following rhombus:

Screen_shot_2014-03-01_at_8.57.04_pm

The perimeter of the rhombus is .

Explanation

The formula for the perimeter of a rhombus is:

Where is the length of the side

Plugging in our values, we get:

The formula for the area of a rhombus is:

Where is the length of one diagonal and is the length of another diagonal

By drawing the diagonals, we create a right triangle with the hypotenuse as and the side as .

Since we know that is a phythagorean triple, we can infer that the third side is .

Plugging in our values, we get:

6

Find the area of the following rhombus:

Screen_shot_2014-03-01_at_8.57.04_pm

The perimeter of the rhombus is .

Explanation

The formula for the perimeter of a rhombus is:

Where is the length of the side

Plugging in our values, we get:

The formula for the area of a rhombus is:

Where is the length of one diagonal and is the length of another diagonal

By drawing the diagonals, we create a right triangle with the hypotenuse as and the side as .

Since we know that is a phythagorean triple, we can infer that the third side is .

Plugging in our values, we get:

7

Find the area of the following kite:

Kite

Explanation

The formula for the area of a kite is:

Where is the length of one diagonal and is the length of the other diagonal

Plugging in our values, we get:

8

Find the area of the following kite:

Kite

Explanation

The formula for the area of a kite is:

Where is the length of one diagonal and is the length of the other diagonal

Plugging in our values, we get:

9

Find the area of the following kite:

Kite

Explanation

The formula for the area of a kite is:

Where is the length of one diagonal and is the length of the other diagonal

Plugging in our values, we get:

10

Erin is getting ready to plant her tulip garden. She wants to plant two tulips per square foot of garden. If her rectangular garden is enclosed by 24 feet of fencing, and the length of the fence is twice as long as its width, how many tulips will Erin plant?

64

48

32

24

16

Explanation

We know that the following represents the formula for the perimeter of a rectangle:

In this particular case, we are told that the length of the fence is twice as long as the width. We can write this as the following expression:

Use this information to substitute in a variable for the length that matches the variable for width in our perimeter equation.

We also know that the length is two times the width; therefore, we can write the following:

The area of a rectangle is found by using this formula:

The area of the garden is 32 square feet. Erin will plant two tulips per square foot; thus, she will plant 64 tulips.

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