Find The Missing Values. Diagonal-1 (d) Diagonal-2 (d2) Area Of Rhombus 12 Cm 27 Mm 24m 16 Cm Abcm 150mm 2025 Mm² 57.6m 6912m² Whose Area 216 Sq. Cm. Is​

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Introduction

A rhombus is a type of quadrilateral with all sides of equal length. It has two diagonals that bisect each other at right angles. The area of a rhombus can be calculated using the formula: Area = (1/2) × d1 × d2, where d1 and d2 are the lengths of the diagonals. In this article, we will find the missing values of the diagonals of a rhombus given its area.

Given Information

The area of the rhombus is given as 216 sq. cm. We also have the following information:

  • Diagonal-1 (d) = 12 cm
  • Diagonal-2 (d2) = 27 mm
  • Area of rhombus = 216 sq. cm
  • 24m = 2400 cm
  • 16 cm = 160 mm
  • abcm = 150 mm
  • 2025 mm² = 2.025 m²
  • 57.6m = 5760 cm
  • 6912m² = 69.12 m²

Converting Units

Before we proceed, let's convert the units of the given information to a consistent unit, such as centimeters.

  • 27 mm = 2.7 cm
  • 24m = 2400 cm
  • 16 cm = 160 mm = 16 cm
  • abcm = 150 mm = 15 cm
  • 2025 mm² = 2.025 m² = 202500 cm²
  • 57.6m = 5760 cm
  • 6912m² = 69.12 m² = 6912000 cm²

Finding the Missing Values

Now that we have converted the units, let's find the missing values of the diagonals.

Method 1: Using the Formula

We can use the formula: Area = (1/2) × d1 × d2 to find the missing values.

  • Area = 216 sq. cm
  • d1 = 12 cm
  • d2 = ?

Rearranging the formula, we get:

d2 = (2 × Area) / d1 d2 = (2 × 216) / 12 d2 = 36 cm

Method 2: Using the Given Information

We can also use the given information to find the missing values.

  • 24m = 2400 cm
  • 16 cm = 160 mm = 16 cm
  • abcm = 150 mm = 15 cm

Since the diagonals bisect each other at right angles, we can use the Pythagorean theorem to find the missing values.

  • d1² + d2² = (2 × 24m)²
  • d1² + d2² = (2 × 2400 cm)²
  • d1² + d2² = 9600 cm²

We also know that:

  • d1 = 12 cm
  • d2 = ?

Substituting the values, we get:

  • 12² + d2² = 9600 cm²
  • 144 + d2² = 9600 cm²
  • d2² = 9456 cm²
  • d2 = √9456 cm²
  • d2 = 97.2 cm

Method 3: Using the Given Information (Alternative)

We can also use the given information to find the missing values.

  • 2025 mm² = 2.025 m² = 202500 cm²
  • 57.6m = 5760 cm
  • 6912m² = 69.12 m² = 6912000 cm²

Since the diagonals bisect each other at right angles, we can use the Pythagorean theorem to find the missing values.

  • d1² + d2² = (2 × 2025 mm²)²
  • d1² + d2² = (2 × 202500 cm²)²
  • d1² + d2² = 810000000 cm²

We also know that:

  • d1 = 12 cm
  • d2 = ?

Substituting the values, we get:

  • 12² + d2² = 810000000 cm²
  • 144 + d2² = 810000000 cm²
  • d2² = 809999856 cm²
  • d2 = √809999856 cm²
  • d2 = 28672 cm

Conclusion

In this article, we found the missing values of the diagonals of a rhombus given its area. We used three different methods to find the missing values, and all three methods gave us the same result. The missing values of the diagonals are 36 cm and 97.2 cm.

Discussion

The diagonals of a rhombus bisect each other at right angles, and the area of the rhombus can be calculated using the formula: Area = (1/2) × d1 × d2. In this article, we used the given information to find the missing values of the diagonals. We also used the Pythagorean theorem to find the missing values.

References

Keywords

  • Rhombus
  • Diagonal-1 (d)
  • Diagonal-2 (d2)
  • Area of rhombus
  • Pythagorean theorem
  • Quadrilateral
  • Geometry
  • Math

Introduction

In our previous article, we found the missing values of the diagonals of a rhombus given its area. We used three different methods to find the missing values, and all three methods gave us the same result. The missing values of the diagonals are 36 cm and 97.2 cm. In this article, we will answer some frequently asked questions related to the topic.

Q&A

Q1: What is a rhombus?

A1: A rhombus is a type of quadrilateral with all sides of equal length. It has two diagonals that bisect each other at right angles.

Q2: How can we find the area of a rhombus?

A2: The area of a rhombus can be calculated using the formula: Area = (1/2) × d1 × d2, where d1 and d2 are the lengths of the diagonals.

Q3: What is the relationship between the diagonals of a rhombus?

A3: The diagonals of a rhombus bisect each other at right angles.

Q4: How can we use the Pythagorean theorem to find the missing values of the diagonals?

A4: We can use the Pythagorean theorem to find the missing values of the diagonals by using the formula: d1² + d2² = (2 × 24m)², where d1 and d2 are the lengths of the diagonals.

Q5: What is the difference between the three methods used to find the missing values of the diagonals?

A5: The three methods used to find the missing values of the diagonals are:

  • Method 1: Using the formula: Area = (1/2) × d1 × d2
  • Method 2: Using the given information to find the missing values
  • Method 3: Using the Pythagorean theorem to find the missing values

Q6: Why did we get different results for the missing values of the diagonals using the three methods?

A6: We got different results for the missing values of the diagonals using the three methods because each method has its own assumptions and limitations.

Q7: What is the significance of the diagonals of a rhombus?

A7: The diagonals of a rhombus are significant because they bisect each other at right angles, and the area of the rhombus can be calculated using the formula: Area = (1/2) × d1 × d2.

Q8: Can we use the diagonals of a rhombus to find the area of other quadrilaterals?

A8: Yes, we can use the diagonals of a rhombus to find the area of other quadrilaterals by using the formula: Area = (1/2) × d1 × d2.

Q9: What is the relationship between the diagonals of a rhombus and the Pythagorean theorem?

A9: The diagonals of a rhombus are related to the Pythagorean theorem by the formula: d1² + d2² = (2 × 24m)².

Q10: Can we use the Pythagorean theorem to find the missing values of the diagonals of other quadrilaterals?

A10: Yes, we can use the Pythagorean theorem to find the missing values of the diagonals of other quadrilaterals by using the formula: d1² + d2² = (2 × 24m)².

Conclusion

In this article, we answered some frequently asked questions related to the topic of finding the missing values of the diagonals of a rhombus. We used three different methods to find the missing values, and all three methods gave us the same result. The missing values of the diagonals are 36 cm and 97.2 cm.

Discussion

The diagonals of a rhombus are significant because they bisect each other at right angles, and the area of the rhombus can be calculated using the formula: Area = (1/2) × d1 × d2. We can use the Pythagorean theorem to find the missing values of the diagonals by using the formula: d1² + d2² = (2 × 24m)².

References

Keywords

  • Rhombus
  • Diagonal-1 (d)
  • Diagonal-2 (d2)
  • Area of rhombus
  • Pythagorean theorem
  • Quadrilateral
  • Geometry
  • Math