High School Homework Helper

Of course! Let's tackle each problem one by one. --- **1. Area of a Rectangle:** To find the area of a rectangle, you multiply its length by its breadth. **Formula**: Area = length × breadth Given: length = 10 units, breadth = 5 units Plugging in the values: Area = 10 units × 5 units = 50 square units **Explanation**: Think of the rectangle as a grid. If you have a rectangle that is 10 units long and 5 units wide, you can fit 50 squares of 1 unit by 1 unit inside that rectangle. That's why the area is 50 square units. --- **2. Perimeter of a Circle:** To determine the perimeter (or circumference) of a circle, you use the formula: **Formula**: \(C = 2πr\) Where: - \(C\) is the circumference of the circle - \(π\) (Pi) is a constant approximately equal to 3.14159 - \(r\) is the radius of the circle Given: \(r = 7\) units Plugging in the values: \(C = 2 × 3.14159 × 7\) \(C ≈ 43.982\) units **Explanation**: Pi (π) represents the ratio of the circumference of any circle to its diameter. The value is the same for every circle. In this formula, by multiplying π by the diameter (or 2 times the radius), you get the entire distance around the circle, which is its circumference. --- **3. Area of a Triangle:** To find the area of a triangle with a given base and height, you use the formula: **Formula**: Area = \( \frac{1}{2} \) × base × height Given: base = 8 units, height = 6 units Plugging in the values: Area = \( \frac{1}{2} \) × 8 units × 6 units = 24 square units **Explanation**: Imagine you have a rectangle with the same base and height as the triangle. The triangle would take up half of that rectangle's area, because a triangle is essentially half of a rectangle when you consider its base and height. Therefore, we multiply the base by the height and then take half of that result to find the area of the triangle. --- I hope these explanations help clarify things for you! Remember, with geometric shapes, these formulas are tools to help you understand the properties and dimensions of the shapes. As you work with them more, they'll become more intuitive. If you have any more questions, don't hesitate to ask!