In a parallelogram it is being given that base = 14 dm and height 6.5 dm. Find its area in(i) `cm^(2)` . (ii) `m^(2)` .

Answer

To find the area of the parallelogram given the base and height, we can follow these steps:

### Given:
- Base (b) = 14 dm
- Height (h) = 6.5 dm

### Step 1: Convert the base and height from decimeters to centimeters for part (i).
1 dm = 10 cm
- Convert base:
\[ b = 14 \, \text{dm} \times 10 = 140 \, \text{cm} \]
- Convert height:
\[ h = 6.5 \, \text{dm} \times 10 = 65 \, \text{cm} \]

### Step 2: Use the area formula for a parallelogram.
The formula for the area (A) of a parallelogram is:
\[ A = \text{Base} \times \text{Height} \]
Substituting the values we found:
\[ A = 140 \, \text{cm} \times 65 \, \text{cm} \]

### Step 3: Calculate the area in square centimeters.
\[ A = 9100 \, \text{cm}^2 \]

### Part (i) Answer:
The area of the parallelogram is \( 9100 \, \text{cm}^2 \).

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### Step 4: Convert the base and height from decimeters to meters for part (ii).
1 dm = 0.1 m
- Convert base:
\[ b = 14 \, \text{dm} \div 10 = 1.4 \, \text{m} \]
- Convert height:
\[ h = 6.5 \, \text{dm} \div 10 = 0.65 \, \text{m} \]

### Step 5: Use the area formula for a parallelogram again.
Substituting the values in meters:
\[ A = 1.4 \, \text{m} \times 0.65 \, \text{m} \]

### Step 6: Calculate the area in square meters.
\[ A = 0.91 \, \text{m}^2 \]

### Part (ii) Answer:
The area of the parallelogram is \( 0.91 \, \text{m}^2 \).

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