How to calculate the area of a rhombus

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HOW TO CALCULATE RHOMBUS AREA

Rhombus, what is it, its properties? How to calculate the area of a rhombus? This article will help you reinforce your elementary geometry knowledge.

Rhombus is a quadrilateral with 4 equal sides, 2 pairs of parallel sides, where opposite angles are equal, and there are no right angles, two perpendicular diagonals intersecting at their midpoint. Another definition is: A rhombus is a special case of a parallelogram when 2 adjacent sides have equal lengths. Here's how to calculate the area of a rhombus, some problem types applying the area formula, and illustrative examples.

Formula for calculating the area of a rhombus

HOW TO CALCULATE RHOMBUS AREA

The standard formula for calculating the area of a rhombus: A= 1⁄2 d1d2 (The area of a rhombus equals half the product of the lengths of its diagonals, the unit of area is square meter m²)

To find the area of a rhombus, you need to know the lengths of its 2 diagonals. Here are some applied exercises:

Example 1: Calculate the area of a rhombus given that diagonal d1 is 5cm long, and diagonal d2 is twice the length of d1.

Solution:

The problem states that d1 is 5cm, and d2 is twice the length of d1, so d2 = 5 x 2 = 10 cm.

Applying the rhombus area formula, we get: A = 1⁄2 d1d2 = 5 x 10 = 50 cm²

Example 2: Calculate the area of a rhombus given side length a is 7 cm, diagonal d2 = 6 cm, and triangle ABC with altitude AH = 5 cm.

Solution:

To calculate the area, first find the length of the remaining diagonal.

According to the properties of a rhombus, the diagonals intersect at the midpoint. Therefore, we have AH = HD = 5 cm. Hence, diagonal d1 = 10cm.

Using the rhombus area formula, we get: A = 1⁄2 d1d2 = 10 x 6 = 60 cm²

The answer is 60 cm²

There are many other types of rhombus area problems based on the lengths of sides, angles that we will learn in higher grades. Then, we need to use the Pythagorean theorem or trigonometric formulas.

In this article, Mytour.vn shares and helps reinforce your knowledge about rhombuses. If you encounter different types of problems requiring the calculation of the perimeter or area of a rhombus, feel free to comment for assistance.

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Rhombuses, squares, parallelograms... are all special cases of quadrilaterals. However, depending on the specific cases, the methods for calculating quadrilateral areas vary.

Frequently Asked Questions

What are the key properties that define a rhombus?

A rhombus is a unique quadrilateral characterized by having four equal sides and two pairs of parallel sides. It also features opposite angles that are equal and two diagonals that intersect at right angles, dividing each other into equal lengths.

How do you calculate the area of a rhombus using its diagonals?

To find the area of a rhombus, you can use the formula A = 1/2 d1 × d2, where d1 and d2 represent the lengths of the two diagonals. This formula highlights that the area is half the product of the diagonals' lengths, measured in square meters.

Can the area of a rhombus be calculated if only one diagonal is known?

No, you cannot calculate the area of a rhombus with just one diagonal's length. To find the area, you need the lengths of both diagonals to apply the area formula correctly.

What method should I use to find the area of a rhombus when side length is given?

If you know the side length of a rhombus but not the diagonals, you can use the Pythagorean theorem to find the diagonals. Once you have both diagonal lengths, you can then apply the formula A = 1/2 d1 × d2 to calculate the area.

What is the relationship between rhombuses, squares, and parallelograms?

Rhombuses, squares, and parallelograms are all types of quadrilaterals. A rhombus is a special case of a parallelogram with equal side lengths, while a square is a specific type of rhombus that also has right angles.

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