1. Problem: Find the perimeter and area of a rectangle with length 15 cm and width 8 cm. 2. Formula: - Perimeter of rectangle = $2(\text{length} + \text{width})$ - Area of rectangle = $\text{length} \times \text{width}$ 3. Calculation: - Perimeter = $2(15 + 8) = 2 \times 23 = 46$ cm - Area = $15 \times 8 = 120$ cm$^2$ 4. Explanation: The perimeter is the total distance around the rectangle, so we add length and width and multiply by 2. The area is the space inside, found by multiplying length by width. 1. Problem: A triangle has sides 7 cm, 24 cm, and 25 cm. Find its perimeter and area. 2. Formula: - Perimeter of triangle = sum of all sides - Area of right triangle = $\frac{1}{2} \times \text{base} \times \text{height}$ 3. Check if triangle is right angled using Pythagoras: $7^2 + 24^2 = 49 + 576 = 625 = 25^2$ 4. Calculation: - Perimeter = $7 + 24 + 25 = 56$ cm - Area = $\frac{1}{2} \times 7 \times 24 = 84$ cm$^2$ 5. Explanation: Since the triangle satisfies Pythagoras theorem, it is right angled. We use base and height as the two shorter sides to find area. 1. Problem: Find the perimeter and area of a circle with radius 14 cm. 2. Formula: - Perimeter (circumference) = $2 \pi r$ - Area = $\pi r^2$ 3. Calculation: - Perimeter = $2 \times 3.14 \times 14 = 87.92$ cm - Area = $3.14 \times 14^2 = 3.14 \times 196 = 615.44$ cm$^2$ 4. Explanation: The perimeter is the distance around the circle, and area is the space inside. We use $\pi \approx 3.14$ for calculations. These problems are challenging and cover different shapes and formulas for perimeter and area.