What's its name? Rhombus, kite, or diamond? ;)

Question Types:

What's its name? Rhombus, kite, or diamond? ;)

Between us... it doesn't matter. It's about that mysterious geometric figure that reminds us of a precious diamond or a deck of cards... Whatever you call it, you must know the properties of this figure and its uniqueness to solve certain geometric problems. So, let's begin...

Question 1

Given the rhombus in the drawing:

What is the area?

Question 2

Look at the rhombus in the figure.

What is the relationship between the marked angles?

Question 3

Look at the rhombus in the figure.

What is its area?

Question 4

Using the rhombus in the drawing:

Calculate the area?

Question 5

A rhombus has a side length measuring 7 cm.

Is DC equal to 8 cm?

Given the rhombus in the drawing:

What is the area?

Let's remember that there are two ways to calculate the area of a rhombus:

The first is the side times the height of the side.

The second is diagonal times diagonal divided by 2.

Since we are given both diagonals, we calculate it the second way:

$\frac{7\times4}{2}=\frac{28}{2}=14$

14

Look at the rhombus in the figure.

What is the relationship between the marked angles?

Let's remember the different definitions of angles:

Corresponding angles are angles located on the same side of the line that intersects the two parallels and are also situated at the same level with respect to the parallel line they are adjacent to.

Therefore, according to this definition, these are the angles marked with the letter A

Alternate angles are angles located on two different sides of the line that intersects two parallels, and which are also not at the same level with respect to the parallel they are adjacent to.

Therefore, according to this definition, these are the angles marked with the letter B

A - corresponding; B - alternate

Look at the rhombus in the figure.

What is its area?

First, let's remember that according to the properties of a rhombus, all sides of a rhombus are equal,

Therefore, if we define the sides of the rhombus with the letters ABCD,

We can argue that:

AB=BC=CD=DA

We use the perimeter formula:

50 = AB+BC+CD+DA

And we can conclude that

4AB=50

(We can also use any other side, it doesn't matter in this case because they are all equal.)

We divide by four and reveal that:

AB=BC=CD=DA = 12.5

Now let's remember the formula for the area of a rhombus: the height times the side corresponding to the height.

We are given the length of the external height 8,

Now, we can replace in the formula:

8*12.5=100

100 cm²

Using the rhombus in the drawing:

Calculate the area?

Remember there are two options to calculate the area of a rhombus:

1: The diagonal multiplied by the diagonal divided by 2.

2: The base multiplied by the height.

In the question, we are only given the data for one of the diagonals and one of the sides, which means we cannot use either of the above formulas.

We need to find more data. Let's begin by finding the second diagonal:

Remember that the diagonals of a rhombus are perpendicular to one another, which means that they form a 90-degree angle.

Therefore, all the triangles in a rhombus are right-angled.

Now we can focus on the triangle where the side and the height are given, and we will calculate the third side using the Pythagorean theorem:

$a²+b²=c²$Insert the given data:

$3^2+x^2=5^2$$9+x^2=25$$x^2=25-9=16$$x=\sqrt{16}=4$

Now that we have found the second half of the diagonal, we can calculate the area of the rhombus by multiplying the two diagonals together.

Since the diagonals in a rhombus are perpendicular and cross each other, they are equal. Hence, our diagonals are equal:

$3+3=6$$4+4=8$Therefore, the area of the rhombus is:

$\frac{6\times8}{2}=\frac{48}{2}=24$

24

A rhombus has a side length measuring 7 cm.

Is DC equal to 8 cm?

Let's recall the properties of a rhombus. In a rhombus, all sides are equal to each other, therefore DC cannot be equal to 8 cm.

Additionally, in a rhombus, there are 2 pairs of parallel and equal sides. Since the side parallel to AB is CD, it must be equal to 7 cm.

No

Question 1

A rhombus and its external height are shown in the figure below.

The length of each side of the rhombus is 5 cm.

What is its area?

Question 2

In the drawing given a rhombus

The length of each side of the rhombus is 5 cm

The length of the height of the side is 3 cm

What is the area of the rhombus?

Question 3

Calculate the area of the rhombus in the figure below:

Question 4

Given the rhombus in the figure

What is your area?

Question 5

Look at the rhombus in the figure.

What is its area?

A rhombus and its external height are shown in the figure below.

The length of each side of the rhombus is 5 cm.

What is its area?

15 cm².

In the drawing given a rhombus

The length of each side of the rhombus is 5 cm

The length of the height of the side is 3 cm

What is the area of the rhombus?

15 cm².

Calculate the area of the rhombus in the figure below:

10 cm²

Given the rhombus in the figure

What is your area?

36 cm².

Look at the rhombus in the figure.

What is its area?

42 cm²

Question 1

Given the rhombus whose length of its sides is 8 cm

The length of the given height is 5 cm

What is the area of the rhombus?

Question 2

Look at the rhombus in the diagram below.

What is the area of the rhombus?

Question 3

Given the rhombus in the figure

What is your area?

Question 4

In the drawing given a rhombus

The length of the main diagonal 6 cm

The length of the secondary diagonal 4 cm

What is the area of the rhombus?

Question 5

Given the rhombus in the drawing:

What is the area?

Given the rhombus whose length of its sides is 8 cm

The length of the given height is 5 cm

What is the area of the rhombus?

40 cm²

Look at the rhombus in the diagram below.

What is the area of the rhombus?

7.5 cm²

Given the rhombus in the figure

What is your area?

80 cm²

In the drawing given a rhombus

The length of the main diagonal 6 cm

The length of the secondary diagonal 4 cm

What is the area of the rhombus?

12 cm²

Given the rhombus in the drawing:

What is the area?

52