The area of trapezium shape table top is 0.88 m$^2$ and its one parallel side is 1 m and the distance between parallel side is 0.8 m, then its another parallel side is :

Question

Accepted Answer

To determine the length of the other parallel side of the trapezium-shaped table top, we can use the formula for the area of a trapezium:

$$ \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} $$

Given:
- Area = 0.88 m²
- One parallel side ($\text{Base}_1$) = 1 m
- Height (distance between parallel sides) = 0.8 m

We need to find the length of the other parallel side ($\text{Base}_2$).

Substitute the known values into the formula:

$$ 0.88 = \frac{1}{2} \times (1 + \text{Base}_2) \times 0.8 $$

First, simplify the equation:

$$ 0.88 = 0.4 \times (1 + \text{Base}_2) $$

Next, divide both sides by 0.4 to solve for $1 + \text{Base}_2$:

$$ \frac{0.88}{0.4} = 1 + \text{Base}_2 $$

$$ 2.2 = 1 + \text{Base}_2 $$

Subtract 1 from both sides to find $\text{Base}_2$:

$$ \text{Base}_2 = 2.2 - 1 $$

$$ \text{Base}_2 = 1.2 $$

Therefore, the length of the other parallel side is 1.2 m, which corresponds to Option 1.

**Explanation for Incorrect Options:**

- **Option 2 (0.1 m):** If the other parallel side were 0.1 m, the calculation would be:
  $$ \frac{1}{2} \times (1 + 0.1) \times 0.8 = 0.44 \, \text{m}^2 $$
  This does not match the given area of 0.88 m², so this option is incorrect.

- **Option 3 (2.1 m):** If the other parallel side were 2.1 m, the calculation would be:
  $$ \frac{1}{2} \times (1 + 2.1) \times 0.8 = 1.24 \, \text{m}^2 $$
  This exceeds the given area of 0.88 m², so this option is incorrect.

- **Option 4 (2.5 m):** If the other parallel side were 2.5 m, the calculation would be:
  $$ \frac{1}{2} \times (1 + 2.5) \times 0.8 = 1.4 \, \text{m}^2 $$
  This also exceeds the given area of 0.88 m², so this option is incorrect.

Thus, Option 1 (1.2 m) is the correct answer, as it satisfies the area condition given in the problem.