The area of a trapezium, whose parallel sides are 22 cm and 27 cm respectively and the distance between parallel sides is 10 cm, is :

Q: The area of a trapezium, whose parallel sides are 22 cm and 27 cm respectively and the distance between parallel sides is 10 cm, is :

To determine the area of a trapezium, we use the formula: \[ \text{Area} = \frac{1}{2} \times (\text{Sum of parallel sides}) \times \text{Distance between parallel sides} \] Given: - The lengths of the parallel sides are 22 cm and 27 cm. - The distance between the parallel sides is 10 cm. Substituting these values into the formula: \[ \text{Area} = \frac{1}{2} \times (22 + 27) \times 10 \] \[ \text{Area} = \frac{1}{2} \times 49 \times 10 \] \[ \text{Area} = \frac{1}{2} \times 490 \] \[ \text{Area} = 245 \, \text{sq. cm} \] Therefore, the area of the trapezium is 245 square centimeters, which corresponds to Option 2. **Explanation for why each option is incorrect:** 1. **Option 1 (152 sq. cm):** This option is incorrect because the calculation of the area using the given formula does not result in 152 sq. cm. The correct calculation yields 245 sq. cm. 2. **Option 3 (490 sq. cm):** This option is incorrect because it represents the product of the sum of the parallel sides and the distance between them without dividing by 2. The formula for the area of a trapezium requires dividing by 2, which results in 245 sq. cm, not 490 sq. cm. 3. **Option 4 (560 sq. cm):** This option is incorrect as it does not align with the correct calculation of the trapezium's area using the given dimensions. The correct area is 245 sq. cm, not 560 sq. cm. In conclusion, the correct answer is Option 2, as it accurately reflects the area of the trapezium calculated using the appropriate formula.

Question

Accepted Answer

To determine the area of a trapezium, we use the formula:

$$ \text{Area} = \frac{1}{2} \times (\text{Sum of parallel sides}) \times \text{Distance between parallel sides} $$

Given:
- The lengths of the parallel sides are 22 cm and 27 cm.
- The distance between the parallel sides is 10 cm.

Substituting these values into the formula:

$$ \text{Area} = \frac{1}{2} \times (22 + 27) \times 10 $$

$$ \text{Area} = \frac{1}{2} \times 49 \times 10 $$

$$ \text{Area} = \frac{1}{2} \times 490 $$

$$ \text{Area} = 245 \, \text{sq. cm} $$

Therefore, the area of the trapezium is 245 square centimeters, which corresponds to Option 2.

**Explanation for why each option is incorrect:**

1. **Option 1 (152 sq. cm):** This option is incorrect because the calculation of the area using the given formula does not result in 152 sq. cm. The correct calculation yields 245 sq. cm.

2. **Option 3 (490 sq. cm):** This option is incorrect because it represents the product of the sum of the parallel sides and the distance between them without dividing by 2. The formula for the area of a trapezium requires dividing by 2, which results in 245 sq. cm, not 490 sq. cm.

3. **Option 4 (560 sq. cm):** This option is incorrect as it does not align with the correct calculation of the trapezium's area using the given dimensions. The correct area is 245 sq. cm, not 560 sq. cm.

In conclusion, the correct answer is Option 2, as it accurately reflects the area of the trapezium calculated using the appropriate formula.