Areas — Important Questions

24 cm²

Step 1: Given - diagonal 1 = 8 cm, diagonal 2 = 6 cm. Step 2: Use formula for area of rhombus = (1/2) × d₁ × d₂. Step 3: Calculate area = (1/2) × 8 × 6 = (1/2) × 48 = 24 cm². Step 4: The area is 24 cm². Common mistake: Forgetting the 1/2 factor gives 48 cm² (wrong).

36 cm²

Step 1: Apply the theorem - area of triangle = (1/2) × area of parallelogram when on same base and between same parallels. Step 2: Given parallelogram area = 72 cm². Step 3: Calculate triangle area = (1/2) × 72 = 36 cm². Step 4: The triangle has half the area of the parallelogram. This relationship is fundamental in coordinate geometry.

625 m²

Step 1: Given - side of square = 25 m. Step 2: Apply formula for area of square = side². Step 3: Calculate area = 25² = 25 × 25 = 625 m². Step 4: The area is 625 m². Common mistake: Multiplying by 4 (perimeter formula) gives 100 m² (wrong).

They are equal

Step 1: A median connects a vertex to the midpoint of the opposite side. Step 2: This creates two triangles with equal bases (since midpoint divides the side equally). Step 3: Both triangles have the same height (distance from the vertex to the base). Step 4: Since area = (1/2) × base × height, and both base and height are equal, the areas are equal. This is a fundamental property of medians.