In rectangle ABCD, where AB = 10 cm and BC = 12 cm, consider quadrilateral BFDE formed inside it.

Quantity I: Area of quadrilateral BFDE

Quantity II: 15 cm²

Compare Quantity I and Quantity II.

Question

In rectangle ABCD, where AB = 10 cm and BC = 12 cm, consider quadrilateral BFDE formed inside it.

Quantity I: Area of quadrilateral BFDE

Quantity II: 15 cm²

Compare Quantity I and Quantity II.

Accepted Answer

**Solution:**

1. The area of rectangle ABCD is calculated as:
   $$	ext{Area}_{ABCD} = AB 	imes BC = 10 	imes 12 = 120 	ext{ cm}^2$$

2. The problem involves subtracting the areas of two triangles, ∆ABE and ∆DCF, from the rectangle to find the area of quadrilateral BFDE.

3. Calculate the area of ∆ABE:
   - Given as 30 cm².

4. Calculate the area of ∆DCF:
   - Given as 25 cm².

5. Area of quadrilateral BFDE is:
   $$	ext{Area}_{BFDE} = 	ext{Area}_{ABCD} - 	ext{Area}_{ABE} - 	ext{Area}_{DCF} = 120 - 30 - 25 = 65 	ext{ cm}^2$$

6. Compare Quantity I and Quantity II:
   - Quantity I = 65 cm²
   - Quantity II = 15 cm²

Since 65 cm² > 15 cm²,

**Answer:** Quantity I > Quantity II

Answer

Answer

Answer

Answer