ABCD is a parallelogram having adjacent sides AB = 35 cm and BC = 28 cm . If the distance between its longer sides is 8 cm , find :
(i) the area of the parallelogram
(ii) the distance between its shorts sides

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the properties of the parallelogram
A parallelogram has opposite sides that are equal in length and the area can be calculated using the formula:
\[ \text{Area} = \text{Base} \times \text{Height} \]

### Step 2: Identify the given values
- Length of side AB = 35 cm (longer side)
- Length of side BC = 28 cm (shorter side)
- Distance between the longer sides (height) = 8 cm

### Step 3: Calculate the area of the parallelogram
Using the formula for the area of a parallelogram:
\[ \text{Area} = \text{Base} \times \text{Height} \]
Here, we can take AB as the base:
\[ \text{Area} = AB \times \text{Height} = 35 \, \text{cm} \times 8 \, \text{cm} \]

Calculating this:
\[ \text{Area} = 280 \, \text{cm}^2 \]

### Step 4: Find the distance between the shorter sides
We know that the area of the parallelogram can also be calculated using the shorter side BC as the base. Let's denote the distance between the shorter sides as CF (the height corresponding to base BC).

Using the area calculated earlier:
\[ \text{Area} = BC \times \text{Height (CF)} \]
Substituting the known values:
\[ 280 \, \text{cm}^2 = 28 \, \text{cm} \times \text{CF} \]

### Step 5: Solve for CF
To find CF, we can rearrange the equation:
\[ \text{CF} = \frac{280 \, \text{cm}^2}{28 \, \text{cm}} \]

Calculating this:
\[ \text{CF} = 10 \, \text{cm} \]

### Final Answers:
(i) The area of the parallelogram is \( 280 \, \text{cm}^2 \).
(ii) The distance between the shorter sides is \( 10 \, \text{cm} \).

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