A rectangular courtyard measures 8 and 1/2m by 6 and 1/4m
(a) Find the perimeter of the courtyard.
(b) Find the area of the courtyard.

Let's solve each part of the problem step by step.

### (a) Find the Perimeter of the Courtyard

The perimeter $P$ of a rectangle is given by the formula:
\[
P = 2 \times (\text{length} + \text{width})
\]
Given:
- Length $ = 8 \frac{1}{2} $ meters
- Width $ = 6 \frac{1}{4} $ meters

First, let's convert the mixed numbers to improper fractions:
\[
8 \frac{1}{2} = \frac{17}{2} \text{ meters}
\]
\[
6 \frac{1}{4} = \frac{25}{4} \text{ meters}
\]

Now, plug these values into the perimeter formula:
\[
P = 2 \times \left(\frac{17}{2} + \frac{25}{4}\right)
\]

To add these fractions, we need a common denominator. The least common denominator (LCD) of 2 and 4 is 4:
\[
\frac{17}{2} = \frac{34}{4}
\]

Now add the fractions:
\[
\frac{34}{4} + \frac{25}{4} = \frac{59}{4}
\]

So the perimeter is:
\[
P = 2 \times \frac{59}{4} = \frac{118}{4} = 29 \frac{1}{2} \text{ meters}
\]

### (b) Find the Area of the Courtyard

The area $A$ of a rectangle is given by the formula:
\[
A = \text{length} \times \text{width}
\]
Substitute the given values:
\[
A = \frac{17}{2} \times \frac{25}{4} = \frac{17 \times 25}{8} = \frac{425}{8} \text{ square meters}
\]

Convert the improper fraction to a mixed number:
\[
\frac{425}{8} = 53 \frac{1}{8} \text{ square meters}
\]

### Summary of Results:
- **Perimeter:** $29 \frac{1}{2}$ meters
- **Area:** $53 \frac{1}{8}$ square meters

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. What would be the perimeter if the courtyard's dimensions were doubled?
2. If a garden path 1 meter wide surrounds the courtyard, what is the new area of the courtyard including the path?
3. How much fencing would be needed to enclose two courtyards of the same size?
4. If the courtyard's length was decreased by 2 meters, what would be the new area?
5. How much would it cost to tile the entire courtyard if the cost per square meter is $10?

**Tip:** Always make sure to convert mixed numbers to improper fractions for easier calculations, especially when dealing with areas and perimeters.

Learn how to calculate the perimeter and area of a rectangular courtyard measuring 8 and 1/2 meters by 6 and 1/4 meters. Includes step-by-step solutions using fractions and geometry concepts. Suitable for Grades 6-8 students.

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