Worksheet: Finding the Area of a Rhombus Using Diagonals

In this worksheet, we will practice finding the area of a rhombus in terms of its diagonal lengths as half the product of these lengths.

Q1:

The height of a rhombus is 4.1 cm, its base length is 6.6 cm, and the length of one of its diagonals is 4.3 cm. Find, to the nearest tenth, the length of the other diagonal.

Q2:

The figure shows a rhombus within a rectangle. Find the area of the rhombus to two decimal places.

Q3:

A rhombus has diagonals 25 and 11. What is its area?

  • A 2 7 5 2
  • B36
  • C550
  • D72
  • E275

Q4:

Given that 𝐶𝐹=3.8cm and 𝐵𝐹=5.7cm, find the area of 𝐴𝐵𝐶𝐷 approximated to the nearest hundredth.

Q5:

In the rhombus 𝐴𝐵𝐶𝐷, the side length is 8.5 cm, and the diagonal lengths are 13 cm and 11 cm. Find the length of 𝐷𝐹. Round your answer to the nearest tenth.

Q6:

Find the area of the rhombus 𝐴𝐵𝐶𝐷 given the diagonals intersect at the point 𝑀 where 𝐴𝐵=14cm and 𝐴𝑀=4cm. Give the answer to two decimal places.

Q7:

A diagonal of a rhombus has length 2.1, while the longer one is four times as long. What is its area?

Q8:

One diagonal of a rhombus has length 11. If the area is 297, what is the length of the other diagonal?

Q9:

A rhombus has height 10 and is such that the product of the lengths of its diagonals is 190. What is the length of its side?

Q10:

Determine the difference in area between a square having a diagonal of 10 cm and a rhombus having diagonals of 2 cm and 12 cm.

Q11:

In the rhombus shown, 𝑋𝑍=8 and 𝑌𝑊=6. What is its area?

Q12:

In the figure, 𝐴𝐶=5.6 and 𝐵𝐸=5.3. What is the area of 𝐴𝐵𝐶𝐷?

Q13:

The product of the lengths of the diagonals of a rhombus is 116. If the height is 7, what is the rhombus’ length, to the nearest hundredth?

Q14:

A rhombus has a perimeter of 168 and one of its diagonals has a length of 41. What is its area? Round your answer to two decimal places.

Q15:

The diagonals of a rhombus have lengths of 16 cm and 21 cm. Find the area of the rhombus giving the answer to one decimal place.

Q16:

Find the area of a rhombus 𝐴𝐵𝐶𝐷 where 𝐴𝐶=60cm and 𝐵𝐷=32cm giving the answer to the nearest square centimeter.

Q17:

Two pieces of land have the same area. The first is in the shape of a square, and the second is in the shape of a rhombus having diagonal lengths of 32 m and 81 m. Calculate the perimeter of the square piece of land.

Q18:

Two plots of land have the same area. One is a square, and the other is a rhombus with diagonals of lengths 48 m and 35 m. What is the perimeter of the square plot? Give your answer to two decimal places.

Q19:

A rhombus has diagonals 23 and 11. What is its area?

  • A 2 5 3 2
  • B34
  • C506
  • D68
  • E253

Q20:

A rhombus has diagonals 23 and 12. What is its area?

  • A 1 3 8
  • B35
  • C552
  • D70
  • E276

Q21:

A rhombus has diagonals 19 and 17. What is its area?

  • A 3 2 3 2
  • B36
  • C646
  • D72
  • E323

Q22:

A parallelogram of base width 2.8 and corresponding height 3 has the same area as a rhombus with one diagonal of length 5. What is the length of the second diagonal to the nearest hundredth?

  • A3.36
  • B4.67
  • C0.84
  • D1.68

Q23:

Determine the area of the rhombus 𝐴𝐵𝐶𝐷. (unit length =1cm)

  • A20 cm2
  • B5 cm2
  • C14 cm2
  • D40 cm2

Q24:

In the figure, 𝑋𝑌𝑍𝑊 is a rhombus and 𝐴𝐵𝐶𝐷 a rectangle. Find the shaded area, given that 𝑋𝑍=4, 𝑌𝑊=6, and 𝐴𝐵=10.

Q25:

One diagonal of a rhombus is twice the length of the other diagonal. If the area of the rhombus is 81 square millimeters, what are the lengths of the diagonals?

  • A20 mm and 40 mm
  • B6 mm and 12 mm
  • C18 mm and 36 mm
  • D9 mm and 18 mm
  • E13 mm and 26 mm

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