The area of a rhombus is an important concept in Grade 5–6 geometry. A rhombus does not provide its height directly, so the easiest way to measure its area is by using its two diagonals. This method is simple, visual, and very easy for students to understand when explained with clear diagrams.
In this lesson, students will learn what a rhombus is, how its diagonals work, why the formula makes sense, and how to calculate the area through step-by-step examples. Practice exercises and answer keys are included to help build understanding and confidence.
Table of Contents
What Is a Rhombus? (Simple Definition)
A rhombus is a quadrilateral with four sides that all have the same length. It looks a bit like a “tilted” square. Unlike a square, the angles of a rhombus are not always right angles.
Important facts about a rhombus:
All four sides are equal in length.
Opposite angles are equal.
Its diagonals cross at a right angle (90°).
The diagonals are essential for finding the area.
A rhombus can be wide, narrow, or tilted, but its equal sides remain the same.
The Diagonals of a Rhombus
A rhombus has two diagonals that connect opposite vertices. These diagonals cross in the center and form a right angle.
We label them:
D = the longer diagonal
d = the shorter diagonal
These two diagonals give us everything we need to calculate its area.
Area Formula of a Rhombus
The area of a rhombus can be found using the following formula:
A = (D × d) ÷ 2
D = long diagonal
d = short diagonal
A = area of the rhombus
The area is half the product of the two diagonals.
Why This Formula Works (Simple Visual Explanation)
A rhombus can be understood by starting with a rectangle. If you draw a rectangle and connect the midpoints of its sides, you create a rhombus in the center and four small triangles in the corners.
These four triangles all have the same shape and the same area. If you cut them out and rearrange them, they fit together perfectly to form a second rhombus identical to the one in the middle.
This means:
Area of the rectangle = Area of rhombus 1 + Area of rhombus 2
Area of the rectangle = 2 × Area of the rhombus
The rectangle’s dimensions match the diagonals of the rhombus:
The length of the rectangle equals the long diagonal D.
The width of the rectangle equals the short diagonal d.
So,
Area of the rectangle = D × d
Area of one rhombus = (D × d) ÷ 2
This visual explanation helps students understand why the formula makes sense.
Steps to Calculate the Area of a Rhombus
Step 1: Identify the long diagonal D and the short diagonal d.
Step 2: Multiply the diagonals (D × d).
Step 3: Divide the result by 2.
Step 4: Write the answer using the correct unit (square units such as cm², in², or m²).
Examples
Example 1
D = 6 cm
d = 4 cm
A = (6 × 4) ÷ 2 = 12 cm²
Example 2
D = 15 cm
d = 10 cm
A = (15 × 10) ÷ 2 = 75 cm²
Example 3
D = 8 in
d = 12 in
A = (8 × 12) ÷ 2 = 48 in²
Common Mistakes Students Make
Using the side length instead of the diagonals.
Forgetting to divide by 2.
Using diagonals that are not in the same unit.
Writing cm instead of cm².
Mixing up the two diagonals.
Practice Exercises
- D = 10 cm, d = 6 cm. Find the area.
- D = 14 in, d = 9 in. Find the area.
- D = 7 cm, d = 11 cm. Find the area.
- D = 25 mm, d = 4 cm. Convert units, then find the area.
- A rhombus has an area of 36 cm² and D = 9 cm. Find d.
- A kite-shaped field is a rhombus with D = 32 m and d = 20 m. Find the area.
Answer Key
- A = (10 × 6) ÷ 2 = 30 cm²
- A = (14 × 9) ÷ 2 = 63 in²
- A = (7 × 11) ÷ 2 = 38.5 cm²
- 4 cm = 40 mm
A = (25 × 40) ÷ 2 = 500 mm² - 36 = (9 × d) ÷ 2 → 72 = 9d → d = 8 cm
- A = (32 × 20) ÷ 2 = 320 m²
Conclusion
Once students understand how diagonals work, finding the area of a rhombus becomes very simple. The formula A = (D × d) ÷ 2 is easy to apply, and the visual explanation helps make the concept clear. With practice, students will become comfortable using diagonals to measure the surface of a rhombus.
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Teacher’s Note
Encourage students to draw the rhombus and label D and d before calculating. Visual support helps eliminate confusion. If possible, use paper cutting to show how two rhombuses form a rectangle. This hands-on activity strengthens understanding and makes the formula memorable.
FAQ : area of a rhombus
What is a diagonal?
A diagonal connects opposite vertices of a shape. A rhombus has two diagonals that cross at a right angle.
Do I need the height to find the area?
No. The diagonals alone are enough.
What units are used for area?
Square units such as cm², in², m², or mm².
Can I use the side length to find the area?
No, not at Grade 5–6 level. The diagonals are required.
Do the diagonals need to be in the same unit?
Yes, always convert before multiplying.
How do you calculate the area of a square?
To find the area of a square, multiply one side by itself.
If the side length is s, then:
Area of a square = s × s = s²
How do you calculate the area of a rectangle?
To find the area of a rectangle, multiply the length by the width.
Area of a rectangle = length × width
How do you calculate the area of a rhombus?
The area of a rhombus is found using its diagonals.
Use the formula:
Area of a rhombus = (D × d) ÷ 2
D = long diagonal
d = short diagonal
How do you calculate the area of a triangle?
To find the area of a triangle, multiply the base by the height and then divide by 2.
If the base is b and the height is h, then:
Area of a triangle = (b × h) ÷ 2
