Area of Rhombus: Questions with Answers

Area of Rhombus: Questions with Answers is a useful topic for students who want to learn geometry in a simple way. Area of Rhombus helps you find the space inside a rhombus using easy formulas and clear steps. This topic is important because it builds a strong base in maths and improves problem solving skills. Students can practise different questions to understand how the formula works in real sums.

Area of Rhombus Formula

Formula Using Diagonals

Area = (d₁ × d₂) / 2

Where:

d₁ = first diagonal

d₂ = second diagonal

d₁ (horizontal diagonal)

d₂ (vertical diagonal)

Area = (AC × BD) / 2

Formula Using Base and Height

Area = Base × Height

Area = b × h

 

Where:

b = length of any side (base)

h = perpendicular height

 

Area = b × h

Basic Area of Rhombus Questions

Find the Area Using Diagonals

Question 1: A rhombus has diagonals of length 8 cm and 6 cm. Find its area.

Given: d₁ = 8 cm, d₂ = 6 cm

Area = (d₁ × d₂) / 2

     = (8 × 6) / 2

     = 48 / 2

     = 24 cm²

Answer: Area = 24 cm²

Question 2: Find the area of a rhombus with diagonals 14 cm and 10 cm.

Given: d₁ = 14 cm, d₂ = 10 cm

Area = (14 × 10) / 2

     = 140 / 2

     = 70 cm²

Answer: Area = 70 cm²

Question 3: The diagonals of a rhombus measure 20 m and 15 m. Find the area.

Given: d₁ = 20 m, d₂ = 15 m

Area = (20 × 15) / 2

     = 300 / 2

     = 150 m²

Answer: Area = 150 m²

Question 4: A rhombus has diagonals of 9 cm and 12 cm. Find its area.

Area = (9 × 12) / 2

     = 108 / 2

     = 54 cm²

Answer: Area = 54 cm²

Find the Area Using Base and Height

Question 5: A rhombus has a base of 7 cm and a height of 5 cm. Find its area.

Given: Base = 7 cm, Height = 5 cm

Area = Base × Height

     = 7 × 5

     = 35 cm²

Answer: Area = 35 cm²

Question 6: Find the area of a rhombus with base 12 m and perpendicular height 9 m.

Area = 12 × 9 = 108 m²

Answer: Area = 108 m²

Question 7: A rhombus-shaped tile has a base of 15 cm and height of 8 cm. Find its area.

Area = 15 × 8 = 120 cm²

Answer: Area = 120 cm²

Missing Measurement Questions

Question 8: The area of a rhombus is 60 cm² and one diagonal is 12 cm. Find the other diagonal.

Given: Area = 60 cm², d₁ = 12 cm, d₂ = ?

Area = (d₁ × d₂) / 2

60 = (12 × d₂) / 2

60 × 2 = 12 × d₂

120 = 12 × d₂

d₂ = 120 / 12

d₂ = 10 cm

Answer: Second diagonal = 10 cm

Question 9: A rhombus has an area of 96 m² and one diagonal of 16 m. Find the other diagonal.

96 = (16 × d₂) / 2

192 = 16 × d₂

d₂ = 192 / 16

d₂ = 12 m

Answer: d₂ = 12 m

Question 10: The area of a rhombus is 84 cm² and its base is 14 cm. Find the height.

Area = Base × Height

84 = 14 × h

h = 84 / 14

h = 6 cm

Answer: Height = 6 cm

Intermediate Area of Rhombus Questions

Word Problems

Question 11: A farmer has a rhombus-shaped field. The two diagonals of the field are 40 m and 30 m. Find the area of the field in square metres. If one bag of seeds covers 50 m², how many bags are needed?

Step 1: Find area of field

Area = (40 × 30) / 2 = 1200 / 2 = 600 m²

Step 2: Find number of seed bags

Bags = 600 / 50 = 12 bags

Answer: Area = 600 m², Bags needed = 12

Question 12: A kite-shaped decoration is made in the form of a rhombus. Its diagonals are 36 cm and 24 cm. Find the area of the decoration.

Area = (36 × 24) / 2

     = 864 / 2

     = 432 cm²

Answer: Area = 432 cm²

Question 13: A rhombus-shaped floor tile has a base of 20 cm and a height of 18 cm. How many tiles are needed to cover a floor of area 72,000 cm²?

Step 1: Area of one tile

Area = 20 × 18 = 360 cm²

Step 2: Number of tiles

= 72,000 / 360 = 200 tiles

Answer: 200 tiles needed

Unit Conversion Questions

Question 14: A rhombus has diagonals of 2 m and 1.5 m. Find the area in cm².

Step 1: Convert to cm

d₁ = 2 m = 200 cm

d₂ = 1.5 m = 150 cm

Step 2: Calculate area

Area = (200 × 150) / 2

     = 30,000 / 2

     = 15,000 cm²

Answer: Area = 15,000 cm²

Question 15: A rhombus has a base of 50 mm and height of 40 mm. Express the area in cm².

Step 1: Convert mm to cm

Base = 50 mm = 5 cm

Height = 40 mm = 4 cm

Step 2: Find area

Area = 5 × 4 = 20 cm²

Answer: Area = 20 cm²

Multi-Step Problems

Question 16: Two rhombuses have the same area of 120 cm². The first has diagonals 20 cm and 12 cm. The second has one diagonal of 15 cm. Find the other diagonal of the second rhombus.

Verify first rhombus:

Area = (20 × 12) / 2 = 120 cm² 

Second rhombus:

120 = (15 × d₂) / 2

240 = 15 × d₂

d₂ = 16 cm

Answer: Second diagonal = 16 cm

Question 17: A rhombus has diagonals in the ratio 3:4. If the area is 216 cm², find both diagonals.

Let d₁ = 3x and d₂ = 4x

Area = (d₁ × d₂) / 2

216 = (3x × 4x) / 2

216 = 12x² / 2

216 = 6x²

x² = 36

x = 6

d₁ = 3 × 6 = 18 cm

d₂ = 4 × 6 = 24 cm

Verification: (18 × 24)/2 = 432/2 = 216 

Answer: d₁ = 18 cm, d₂ = 24 cm

Challenging Area of Rhombus Questions

Application-Based Questions

Question 18: A rhombus-shaped garden has diagonals of 18 m and 12 m. A path of 1 m width runs along the border (perimeter). If each side of the rhombus is 10.82 m, find the area of only the garden (excluding the path).

Step 1: Area of full rhombus (garden + path)

Area = (18 × 12) / 2 = 108 m²

Step 2: For this problem, we use the inner area.

Since path is 1 m wide on all sides:

Inner diagonals = (18 − 2) and (12 − 2) = 16 m and 10 m

(path reduces each half-diagonal by 1)

Inner area = (16 × 10) / 2 = 80 m²

Path area = 108 − 80 = 28 m²

Answer: Garden area (without path) = 80 m²

Question 19: The diagonals of a rhombus are in the ratio 5:12. The perimeter of the rhombus is 104 cm. Find the area.

Perimeter = 4 × side = 104

Side = 26 cm

Let diagonals be 5k and 12k.

Each half-diagonal: 5k/2 and 12k/2

Using Pythagoras (side of rhombus):

(5k/2)² + (12k/2)² = 26²

25k²/4 + 144k²/4 = 676

169k²/4 = 676

k² = 676 × 4/169 = 16

k = 4

d₁ = 5 × 4 = 20 cm

d₂ = 12 × 4 = 48 cm

Area = (20 × 48) / 2 = 960 / 2 = 480 cm²

Answer: Area = 480 cm²

Higher-Order Thinking (HOTS)

Question 20: A rhombus is cut from a rectangle of dimensions 30 cm × 20 cm. The rhombus has diagonals equal to the length and width of the rectangle. Find the area of the remaining pieces.

Area of rectangle = 30 × 20 = 600 cm²

Area of rhombus = (30 × 20) / 2 = 300 cm²

Remaining area = 600 − 300 = 300 cm²

Remaining pieces = 4 corner triangles

Answer: Remaining area = 300 cm²

Question 21: Two congruent rhombuses are placed side by side sharing one side. If each rhombus has diagonals of 10 cm and 8 cm, what is the total area of the combined figure?

Area of one rhombus = (10 × 8) / 2 = 40 cm²

Total area = 2 × 40 = 80 cm²

(The shapes share a side but each has its own area)

Answer: Total area = 80 cm²

Mixed Geometry Problems

Question 22: A rhombus and a triangle have the same area. The rhombus has diagonals 16 cm and 12 cm. The triangle has base 24 cm. Find the height of the triangle.

Area of rhombus = (16 × 12) / 2 = 96 cm²

Triangle area = (1/2) × base × height

96 = (1/2) × 24 × h

96 = 12h

h = 8 cm

Answer: Height of triangle = 8 cm

Area of Rhombus MCQs

Easy MCQs

Q1: A rhombus has diagonals 6 cm and 8 cm. Its area is:

a) 48 cm²    b) 24 cm²    c) 14 cm²    d) 96 cm²

Answer: b) 24 cm²

Solution: (6 × 8)/2 = 24 

Q2: Area of rhombus formula using diagonals is:

a) d₁ + d₂    b) d₁ × d₂    c) (d₁ × d₂)/2    d) 2(d₁ + d₂)

Answer: c) (d₁ × d₂)/2 

Q3: A rhombus with base 9 cm and height 4 cm has area:

a) 13 cm²    b) 36 cm²    c) 18 cm²    d) 26 cm²

Answer: b) 36 cm²

Solution: 9 × 4 = 36

Q4: If d₁ = 10 and d₂ = 10, the area of the rhombus is:

a) 50    b) 100    c) 20    d) 25

Answer: a) 50

Solution: (10 × 10)/2 = 50

Moderate MCQs

Q5: Area of rhombus is 150 cm². One diagonal is 25 cm. The other diagonal is:

a) 10 cm    b) 15 cm    c) 12 cm    d) 6 cm

Answer: c) 12 cm

Solution: 150 = (25 × d₂)/2 → d₂ = 12

Q6: A rhombus has diagonals in ratio 3:4 and area 96 cm². The longer diagonal is:

a) 12 cm    b) 16 cm    c) 8 cm    d) 18 cm

Answer: b) 16 cm

Solution: (3x)(4x)/2 = 96 → x²= 16 → x=4

Longer = 4×4 = 16

Q7: Which rhombus has the greatest area?

a) d₁=10, d₂=8    b) d₁=12, d₂=6    c) d₁=9, d₂=9    d) d₁=15, d₂=5

Area a = (10×8)/2 = 40

Area b = (12×6)/2 = 36

Area c = (9×9)/2 = 40.5

Area d = (15×5)/2 = 37.5

Answer: c) d₁=9, d₂=9 has area 40.5 cm² 

Q8: The perimeter of a rhombus is 40 cm. Its height is 6 cm. The area is:

a) 240 cm²    b) 60 cm²    c) 120 cm²    d) 30 cm²

Answer: b) 60 cm²

Solution: Side = 40/4 = 10 cm; Area = 10 × 6 = 60 

Q9: A rhombus has one diagonal double the other. If area = 100 cm², the diagonals are:

a) 5, 10    b) 10, 20    c) 8, 16    d) 20, 40

Let d₁ = x, d₂ = 2x

(x × 2x)/2 = 100

2x²/2 = 100

x² = 100

x = 10

Answer: b) 10 cm and 20 cm

Q10: If each diagonal of a rhombus is increased by 50%, the area increases by:

a) 50%    b) 100%    c) 125%    d) 150%

Original area = (d₁ × d₂)/2

New diagonals = 1.5d₁ and 1.5d₂

New area = (1.5d₁ × 1.5d₂)/2 = 2.25 × original

Increase = 125%

Answer: c) 125%

Area of Rhombus Worksheet Questions

Fill in the Blanks

Q1: Area of rhombus = (_____ × _____) / 2

Answer: d₁ × d₂ 

Q2: If diagonals are 10 cm and 8 cm, area = _____ cm²

Answer: 40 cm² 

Q3: Area = Base × _____ 

Answer: Height 

Q4: If area = 72 cm² and one diagonal = 9 cm, other diagonal = _____ cm

Answer: 16 cm 

Q5: A rhombus with base 11 cm and height 5 cm has area _____ cm²

Answer: 55 cm² 

Q6: Total outcomes formula when finding area 

    with base and height: Area = b × ___

Answer: h

Q7: If both diagonals of a rhombus equal 6 cm,

    area = _____ cm²

Answer: 18 cm² 

Q8: The unit of area is always in _____ units.

Answer: square 

Short Answer Questions

Q9: Find the area of a rhombus with diagonals 22 cm and 18 cm.

Area = (22 × 18)/2 = 396/2 = 198 cm²

Q10: A rhombus has base 13 cm and height 7 cm. Find its area.

Area = 13 × 7 = 91 cm²

Q11: The area of a rhombus is 144 cm². Both diagonals are equal. Find each diagonal.

(d × d)/2 = 144

d² = 288

d = √288 = 12√2 ≈ 16.97 cm

Q12: How does the area change if one diagonal is doubled and the other remains the same?

Original area = (d₁ × d₂)/2

New area = (2d₁ × d₂)/2 = d₁ × d₂ = 2 × original

Answer: Area doubles

Long Answer Questions

Q13: A rhombus-shaped plot has diagonals of 50 m and 40 m. The owner wants to: a) Find the total area b) Fence the plot (each side = 32 m, cost = ₹25 per m) c) Grass the entire area (cost = ₹15 per m²)

a) Area = (50 × 40)/2 = 1000 m²

b) Perimeter = 4 × 32 = 128 m

   Fencing cost = 128 × 25 = ₹3,200

c) Grassing cost = 1000 × 15 = ₹15,000

Total cost = 3,200 + 15,000 = ₹18,200

Q14: Compare two rhombuses:

• Rhombus A: diagonals 24 cm and 10 cm

• Rhombus B: base 15 cm, height 8 cm

Which has the greater area? By how much?

Area of Rhombus A = (24 × 10)/2 = 120 cm²

Area of Rhombus B = 15 × 8 = 120 cm²

Both have EQUAL area.

Difference = 0 cm²

Download PDF - Area of Rhombus Questions