# 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.

**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 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 where and 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.

**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 . (unit length )

- A20 cm
^{2} - B5 cm
^{2} - C14
cm
^{2} - D40 cm
^{2}