In a parallelogram, the diagonals are 26 cm and 10 cm and intersect at right angles. Find the side length and the area of the parallelogram.
Show answer & explanation
Correct answer: A
Explanation
Given:
Diagonal₁ = 26 cm
Diagonal₂ = 10 cm
Both diagonals intersect at right angles
By the formula:
Area of a parallelogram = (1/2) × d₁ × d₂
Side = √[(d₁/2)² + (d₂/2)²]
Area = (1/2) × 26 × 10 = 130
Side = √[(26/2)² + (10/2)²]
= √(13² + 5²)
= √(169 + 25)
= √194
Side = √194 cm
Area = 130 cm2