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

**Q4: **

Given that and , find the area of approximated to the nearest hundredth.

**Q5: **

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

**Q6: **

Find the area of the rhombus given the diagonals intersect at the point where and . 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, and . What is its area?

**Q12: **

In the figure, and . What is the area of ?

**Q13: **

The lengths of the diagonals of a rhombus are in the ratio 5 : 6, with the smaller diagonal of length 50. Find the area of the rhombus correct to the nearest hundredth.

**Q14: **

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?

**Q15: **

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.

**Q16: **

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.

**Q17: **

Find the area of a rhombus where and giving the answer to the nearest square centimetre.

**Q18: **

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.

**Q19: **

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.

**Q20: **

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 . What are the dimensions of the new field?

- A 98 m, 88 m
- B 116 m, 87 m
- C 125 m, 93 m
- D 88 m, 66 m