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In this lesson, we will learn how to find the area of a rhombus in terms of its diagonal lengths as a half of 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:

The lengths of the diagonals of a rhombus are in the ratio 5β:β6, with the smaller diagonal of length 50. Find the area of the rhombus correct to the nearest hundredth.

Q4:

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

Q5:

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

Q6:

In the rhombus π΄ π΅ πΆ π· , the side length is 8.5 cm, and the diagonal lengths are 13 cm and 11 cm. Find the length of π· πΉ . Round your answer to the nearest tenth.

Q7:

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

Q8:

A rhombus has diagonals 20 and 2. What is its area?

Q9:

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

Q10:

A rhombus has diagonals 24 and 20. What is its area?

Q11:

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

Q12:

One diagonal of a rhombus has length 8. If the area is 476, what is the length of the other diagonal?

Q13:

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.

Q14:

A diagonal of a rhombus has length 2, while the longer one is four times as long. What is its area?

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 π΄ π΅ πΆ π· where π΄ πΆ = 6 0 c m and π΅ π· = 3 2 c m giving the answer to the nearest square centimetre.

Q17:

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.

Q18:

A field in the shape of a trapezium has parallel sides of lengths 61 m and 67 m which are 68 m apart. Another field is shaped like a rhombus with diagonal lengths 52 m and 56 m. These two fields are to be replaced with a single rectangular field whose area is the sum of the two area with sides in the ratio 4 βΆ 3 . What are the dimensions of the new field?

Q19:

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?

Q20:

In the figure, π΄ πΆ = 5 . 6 and π΅ πΈ = 5 . 3 . What is the area of π΄ π΅ πΆ π· ?

Q21:

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.

Q22:

Given that πΆ πΉ = 2 . 4 c m and π΅ πΉ = 5 c m , find the area of π΄ π΅ πΆ π· approximated to the nearest hundredth.

Q23:

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 40 m and 125 m. Calculate the perimeter of the square piece of land.

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