Class 9 RD Sharma Solutions Chapter 15 Areas of Parallelograms and Triangles Exercise 15.1 (original) (raw)
Last Updated : 4 Sep, 2024
Understanding the areas of parallelograms and triangles is essential in geometry as these shapes are fundamental in various applications. Chapter 15 of RD Sharma's Class 9 mathematics textbook explores the methods to calculate the areas of these shapes. This chapter emphasizes the use of formulas and theorems to find the area accurately and solve related problems efficiently.
Areas of Parallelograms and Triangles
The area of a parallelogram can be determined using the formula Area=base×height where the base is any one of its sides and the height is the perpendicular distance from this base to the opposite side. For triangles, the area is calculated using the Area= 1\2 × base × height. These fundamental concepts are critical in solving geometric problems and applications involving these
**Question 1. Which of the following figures lie on the same base and between the same parallels? In such a case, write the common base and two parallels:
**Solution:
****(i)**
ΔPAB and trapezium ABCD are on the same base AB and between the same parallels AB and DC.
Same base = AB
Parallels = AB || DC
****(ii)**
Parallelogram ABCD and APQD are on the same base AD and between the same parallels AD and BQ.
Same base = AD
Parallels = AD || BQ
****(iii)**
Parallelogram ABCD and ΔPQR are between the same parallels AD and BC but they are not on the same base.
****(iv)**
ΔQRT and parallelogram PQRS are on the same base QR and between the same parallels QR and PS.
Same base = QR
Parallels = QR || PS
****(v)**
Parallelograms PQRS and trapezium SMNR are on the same base but not between same parallels.
****(vi)**
Parallelograms PQRS, AQRD, BCQR are between the same parallels. Also, parallelograms PQRS, BPSC, APSD are between the same parallels.
Conclusion
The Mastering the calculation of areas for the parallelograms and triangles provides the solid foundation for further studies in the geometry and various practical applications. The exercises in this chapter help reinforce these concepts through the practice ensuring students can apply these techniques confidently. Understanding these principles is crucial for the solving more complex geometric problems and real-world scenarios.