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Lesson: Area of a Rhombus

Sample Question Videos

Worksheet • 14 Questions • 1 Video

Q1:

Given a rhombus whose diagonals’ lengths are 5.3 cm and 3.8 cm and a square whose diagonal length is 5.3 cm, which one is smaller in area?

  • Athe square
  • Bthe rhombus

Q2:

𝐴 𝐡 𝐢 𝐷 is a rhombus in which 𝐷 𝐡 = 2 2 . 4 c m . Determine the length of 𝐴 𝐢 and the area of 𝐴 𝐡 𝐢 𝐷 .

  • A 𝐴 𝐢 = 3 6 c m , area = 403.2 cm2
  • B 𝐴 𝐢 = 4 7 . 9 5 c m , area = 537.04 cm2
  • C 𝐴 𝐢 = 1 8 c m , area = 201.6 cm2
  • D 𝐴 𝐢 = 6 . 3 2 c m , area = 806.4 cm2

Q3:

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?

  • A 9 mm and 18 mm
  • B 20 mm and 40 mm
  • C 18 mm and 36 mm
  • D 6 mm and 12 mm
  • E 13 mm and 26 mm

Q4:

A rhombus and a square have the same area. If the square’s perimeter is 44 and one of the diagonals of the rhombus is 10, how long is the other diagonal, to two decimal places?

Q5:

Determine the area of a rhombus if the length of its greater diagonal is 12 cm, and the length of its smaller diagonal equals half the length of its greater one, and approximate the answer to the nearest hundredth, if needed.

Q6:

In the figure, 𝑋 π‘Œ 𝑍 π‘Š is a rhombus and 𝐴 𝐡 𝐢 𝐷 a rectangle. Find the shaded area, given that 𝑋 𝑍 = 4 , π‘Œ π‘Š = 6 , and 𝐴 𝐡 = 1 0 .

Q7:

Find the area of a rhombus with side 41 and height 29.

Q8:

A rhombus has perimeter 116 and area 870. What is its height?

Q9:

Find the height of a rhombus of side 3 and area 96.

Q10:

A rhombus has side 11.6 and height 8.8. What is its area?

Q11:

The perimeter of rhombus 𝐴 𝐡 𝐢 𝐷 is 20. If 𝐹 𝐸 = 4 , what is the area of the rhombus?

  • A20
  • B40
  • C10
  • D8.94
  • E17.89

Q12:

In the figure, suppose that 𝐷 𝐸 = 3 7 c m and 𝐴 𝐡 = 𝐡 𝐢 = 𝐢 𝐷 = 𝐷 𝐴 . What is the area of the quadrilateral 𝐴 𝐡 𝐢 𝐷 ?

Q13:

What is the area of this rhombus?

Q14:

A rhombus has a perimeter of 152 and one of its angles is 7 5 ∘ . What is its area?

  • A 1 394.8
  • B 1 444
  • C134.28
  • D128.09
  • E 1 126.96
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