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 basic area theorems covered in Class 9? |  |
Ans. In Class 9, the basic area theorems include the area of triangles, quadrilaterals, and circles. Students learn how to calculate the area using different formulas based on the shape, such as \( \text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} \), \( \text{Area of rectangle} = \text{length} \times \text{breadth} \), and \( \text{Area of circle} = \pi r^2 \).
| 2. How can I find the area of a triangle using the base and height? | |
Ans. To find the area of a triangle, you can use the formula: \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). Measure the length of the base and the height (the perpendicular distance from the base to the opposite vertex), then substitute these values into the formula to calculate the area.
| 3. What is the difference between the area of a rectangle and a square? | |
Ans. The area of a rectangle is calculated using the formula \( \text{Area} = \text{length} \times \text{breadth} \), while the area of a square is calculated using \( \text{Area} = \text{side}^2 \). A square is a special case of a rectangle where all four sides are equal, making the calculations for area slightly simpler.
| 4. How do I calculate the area of a trapezium? | |
Ans. The area of a trapezium (or trapezoid) can be calculated using the formula: \( \text{Area} = \frac{1}{2} \times (a + b) \times h \), where \( a \) and \( b \) are the lengths of the parallel sides, and \( h \) is the height (the perpendicular distance between the parallel sides). Measure these lengths and substitute them into the formula to find the area.
| 5. Why is it important to learn area theorems in Class 9? | |
Ans. Learning area theorems in Class 9 is important because they form the foundation for understanding more complex geometric concepts in higher classes. These theorems help students develop problem-solving skills, improve their analytical thinking, and apply mathematical concepts in real-world scenarios, such as architecture and engineering.
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Sep 07, 2025
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