Let’s solve each rhombus problem one by one.
Remember:
A
rhombus has 4 equal sides.
To find the
perimeter, we need to find the length of
one side, then multiply by 4.
The diagonals of a rhombus cut each other in half at right angles (90°), so they form 4 right-angled triangles inside the rhombus.
We can use the
Pythagorean theorem to find the side length:
> If the two halves of the diagonals are `a` and `b`, then the side `s = √(a² + b²)`
Then, perimeter = 4 × s
---
Problem 1)
Diagonals: 8 cm and 10 cm
→ Half-diagonals: 4 cm and 5 cm
Side = √(4² + 5²) = √(16 + 25) = √41 ≈ 6.403 cm
Perimeter = 4 × 6.403 ≈ 25.612 →
25.6 cm (to 1 decimal place)
✔ Check: 4²=16, 5²=25, sum=41, sqrt(41)=6.403..., times 4 = 25.612 → rounds to 25.6
---
Problem 2)
Diagonals: 7 cm and 7 cm
→ Half-diagonals: 3.5 cm and 3.5 cm
Side = √(3.5² + 3.5²) = √(12.25 + 12.25) = √24.5 ≈ 4.9497 cm
Perimeter = 4 × 4.9497 ≈ 19.7988 →
19.8 cm
✔ Check: 3.5² = 12.25, doubled is 24.5, sqrt(24.5)≈4.9497, times 4≈19.7988 → rounds to 19.8
---
Problem 3)
Diagonals: 9 cm and 16 cm
→ Half-diagonals: 4.5 cm and 8 cm
Side = √(4.5² + 8²) = √(20.25 + 64) = √84.25 ≈ 9.1788 cm
Perimeter = 4 × 9.1788 ≈ 36.715 →
36.7 cm
✔ Check: 4.5²=20.25, 8²=64, sum=84.25, sqrt≈9.1788, times 4≈36.715 → rounds to 36.7
---
Problem 4)
Diagonals: 14 cm and 26 cm
→ Half-diagonals: 7 cm and 13 cm
Side = √(7² + 13²) = √(49 + 169) = √218 ≈ 14.7648 cm
Perimeter = 4 × 14.7648 ≈ 59.059 →
59.1 cm
✔ Check: 7²=49, 13²=169, sum=218, sqrt≈14.7648, times 4≈59.059 → rounds to 59.1
---
Final Answer:
1) 25.6 cm
2) 19.8 cm
3) 36.7 cm
4) 59.1 cm
Parent Tip: Review the logic above to help your child master the concept of area of a rhombus worksheet.
