Class 9 Exam > Class 9 Notes > Mathematics Class 9 ICSE > Revision Notes: Area Theorems
Revision Notes: Area Theorems | Mathematics Class 9 ICSE PDF Download
- The amount of surface enclosed by the boundary of a plane closed figure is called its area and is measure in squared units.
- A diagonal of a parallelogram divides it into two congruent triangles i.e. two triangles of equal area.
- Parallelograms between the same base and between the same parallels are equal in area.
- A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
- Parallelograms with equal bases and between the same parallels are equal in area.
- If a triangle and a parallelogram are on the same base and between the same parallels, then the area of the triangle is equal to half area of the parallelogram.
- Triangles on the same base and between the same parallels are equal in area.
- Triangles with equal bases and between the same parallels are equal in area.
- Triangles with equal areas and lying on the same or equal bases have equal altitudes.
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FAQs on Revision Notes: Area Theorems - Mathematics Class 9 ICSE
| 1. What are the main area theorems covered in Class 9 mathematics? |  |
Ans. In Class 9 mathematics, the main area theorems include the area of triangles, quadrilaterals, and circles. The key concepts involve understanding how to calculate the area using different formulas, such as the area of a triangle (1/2 * base * height), the area of a rectangle (length * breadth), and the area of a circle (π * radius²).
| 2. How do you find the area of a triangle using the base and height? | |
Ans. To find the area of a triangle, you can use the formula: Area = 1/2 * base * height. You need to measure the length of the base and the perpendicular height from the base to the opposite vertex. Multiply these two values and then divide by 2 to get the area.
| 3. What is the formula for calculating the area of a circle in Class 9? | |
Ans. The formula for calculating the area of a circle is given by Area = π * radius². Here, 'π' is a constant approximately equal to 3.14, and 'radius' is the distance from the center of the circle to any point on its circumference.
| 4. Can you explain how to find the area of a quadrilateral? | |
Ans. The area of a quadrilateral can be found using different methods depending on the type of quadrilateral. For a rectangle, use Area = length * breadth. For a square, use Area = side². For irregular quadrilaterals, you can divide it into simpler shapes (like triangles or rectangles), find their areas, and then sum them up.
| 5. Why is it important to understand area theorems in Class 9? | |
Ans. Understanding area theorems in Class 9 is crucial because they form the foundation for more advanced mathematical concepts. These theorems are not only used in geometry but also in real-life applications such as architecture, engineering, and various fields where spatial measurements are required. Mastery of these concepts helps students develop critical thinking and problem-solving skills.
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