Practice Problems: Identifying Rhombus Properties

Solution:
Area = (10 cm × 16 cm) / 2 
Area = 160 cm² / 2 
Area = 80 cm²

Formula (Pythagorean): s² = (d₁ / 2)² + (d₂ / 2)²

Solution:
The diagonals divide the rhombus into four right-angled triangles. The legs of each triangle are half the diagonals. 
Leg 1 = d₁ / 2 = 6 m / 2 = 3 m 
Leg 2 = d₂ / 2 = 8 m / 2 = 4 m 
The side of the rhombus (s) is the hypotenuse. 
s² = (3 m)² + (4 m)² 
s² = 9 m² + 16 m² 
s² = 25 m² 
s = √25 
s = 5 meters

Formula (Pythagorean): s² = (d₁ / 2)² + (d₂ / 2)²

Solution:
Let s = 10, and d₁ = 16. We need to find d₂. 
The legs of the right triangle are (d₁ / 2) = 8 inches, and (d₂ / 2). The hypotenuse (s) is 10 inches. 
(8)² + (d₂ / 2)² = 10² 
64 + (d₂ / 2)² = 100 
(d₂ / 2)² = 100 - 64 
(d₂ / 2)² = 36 
Take the square root of both sides: 
d₂ / 2 = 6 inches 
Now, solve for the full diagonal d₂: 
d₂ = 6 × 2 
d₂ = 12 inches

Answer: No, not definitely.

A kite also has diagonals that are perpendicular. A rhombus is a special type of kite where all four sides are equal (which also means the diagonals bisect each other).

To be a rhombus, the diagonals must be perpendicular bisectors of each other. Just being perpendicular is not enough information.