Find the best tutors and institutes for Class 10 Tuition
Q5(a):
$PQRS$ is a parallelogram (Fig 9.14). $QM$ is the height from $Q$ to $SR$ and $QN$ is the height from $Q$ to $PS$. If $SR = 12$ cm and $QM = 7.6$ cm. Find: (a) the area of the parallegram $PQRS$.
$PQRS$ is a parallelogram (Fig 9.14). $QM$ is the height from $Q$ to $SR$ and $QN$ is the height from $Q$ to $PS$. If $SR = 12$ cm and $QM = 7.6$ cm. Find: (a) the area of the parallegram $PQRS$.
Solution :
Given Variables & Initial Setup
We are presented with a parallelogram $PQRS$ in Euclidean space, along with specific orthogonal heights (altitudes) corresponding to its bases. The given parameters are structured as follows:
| Geometric Entity | Symbolic Representation | Magnitude / Value |
|---|---|---|
| Base of the Parallelogram | $SR$ | $12 \text{ cm}$ |
| Altitude to Base $SR$ | $QM$ | $7.6 \text{ cm}$ |
| Altitude to Base $PS$ | $QN$ | Unknown (Not required for Part A) |
Step 1: Theoretical Foundation for the Area of a Parallelogram
By the fundamental theorems of planar geometry, a parallelogram can be transformed into a rectangle of equal area by translating a right-angled triangle from one side to the other. Therefore, the area $A$ of any parallelogram is strictly equal to the product of the length of any chosen base ($b$) and its corresponding orthogonal height ($h$).
[Per the Area Axioms of Euclidean Geometry]:
$A = b \times h$
In the context of parallelogram $PQRS$, if we select $SR$ as the base, the corresponding height is the perpendicular distance from the opposite parallel side ($PQ$) to $SR$. This orthogonal segment is explicitly given as $QM$.
$A = SR \times QM$
Step 2: High-Precision Visual Representation
Below is the geometrically scaled representation of parallelogram $PQRS$, mapping the given dimensions and orthogonal projections. The coordinates are calculated to preserve the exact ratio of the base to the height ($12 : 7.6$).
Step 3: Algebraic Substitution and Calculation
We now substitute the known scalar quantities into our established area formula. Ensure that the units are consistent (both are in centimeters), which will yield an area in square centimeters ($\text{cm}^2$).
- Base ($SR$) = $12 \text{ cm}$
- Height ($QM$) = $7.6 \text{ cm}$
Executing the multiplication:
$A = 12 \text{ cm} \times 7.6 \text{ cm}$
To compute this precisely without a calculator, we can decompose the decimal:
$A = 12 \times \left(7 + 0.6\right)$
$A = (12 \times 7) + (12 \times 0.6)$
$A = 84 + 7.2$
$A = 91.2 \text{ cm}^2$
Final Solution: The area of the parallelogram $PQRS$ is $91.2 \text{ cm}^2$.
More Questions from Class 9 Mathematics Coordinate Geometry EXERCISE 9.1
- Q1(a): Find the area of each of the following parallelograms: (a)
- Q1(b): Find the area of each of the following parallelograms: (b)
- Q1(c): Find the area of each of the following parallelograms: (c)
- Q1(d): Find the area of each of the following parallelograms: (d)
- Q1(e): Find the area of each of the following parallelograms: (e)
- Q2(a): Find the area of each of the following triangles: (a)
- Q2(b): Find the area of each of the following triangles: (b)
- Q2(c): Find the area of each of the following triangles: (c)
- Q2(d): Find the area of each of the following triangles: (d)
- Q3(a): Find the missing values: Base = $20$ cm, Height = ______, Area of the Parallelogram = $246$ cm$^2$.
- Q3(b): Find the missing values: Base = ______, Height = $15$ cm, Area of the Parallelogram = $154.5$ cm$^2$.
- Q3(c): Find the missing values: Base = ______, Height = $8.4$ cm, Area of the Parallelogram = $48.72$ cm$^2$.
- Q3(d): Find the missing values: Base = $15.6$ cm, Height = ______, Area of the Parallelogram = $16.38$ cm$^2$.
- Q4(a): Find the missing values: Base = $15$ cm, Height = ______, Area of Triangle = $87$ cm$^2$.
- Q4(b): Find the missing values: Base = ______, Height = $31.4$ mm, Area of Triangle = $1256$ mm$^2$.
- Q4(c): Find the missing values: Base = $22$ cm, Height = ______, Area of Triangle = $170.5$ cm$^2$.
- Q5(b): $PQRS$ is a parallelogram (Fig 9.14). $QM$ is the height from $Q$ to $SR$ and $QN$ is the height from $Q$ to $PS$. If $SR = 12$ cm and $QM = 7.6$ cm. Find: (b) $QN$, if $PS = 8$ cm.
- Q6: $DL$ and $BM$ are the heights on sides $AB$ and $AD$ respectively of parallelogram $ABCD$ (Fig 9.15). If the area of the parallelogram is $1470$ cm$^2$, $AB = 35$ cm and $AD = 49$ cm, find the length of $BM$ and $DL$.
- Q7: $\triangle ABC$ is right angled at $A$ (Fig 9.16). $AD$ is perpendicular to $BC$. If $AB = 5$ cm, $BC = 13$ cm and $AC = 12$ cm, Find the area of $\triangle ABC$. Also find the length of $AD$.
- Q8: $\triangle ABC$ is isosceles with $AB = AC = 7.5$ cm and $BC = 9$ cm (Fig 9.17). The height $AD$ from $A$ to $BC$, is $6$ cm. Find the area of $\triangle ABC$. What will be the height from $C$ to $AB$ i.e., $CE$?
CBSE Solutions for Class 9 Mathematics Coordinate Geometry
Chapters in CBSE - Class 9 Mathematics
Top Tutors who teach Coordinate Geometry
Top Tutor
Jawahar Nagar Sector 5, Jaipur
4 yrs of
Exp
1 student
20 hrs of classes completed
350
per hour
Online Classes
Tutor's home
As a dedicated and experienced educator, I offer personalized class 6 to 10 and till BCA in a supportive online learning environment. With a strong background in Mathematics, Science, and Computers, I am committed to helping students achieve academic excellence and develop a deep understanding of complex concepts. My teaching approach is centered around clarity, simplicity, and innovative methods, ensuring that students of all learning styles feel engaged and motivated. With a proven track record of consistently high academic achievement and a passion for inspiring a love for learning, I am confident in my ability to make a positive impact on my students' academic journeys.
Avdesh sir tailored the lessons to meet my individual needs, making complex topics accessible and engaging.
Top Tutor
Electronic City Electronics City Phase 1, Bangalore
15 yrs of
Exp
5 students
39 hrs of classes completed
1000
per hour
Online Classes
Ph.D enrolled, M.Tech(Electrical eng). Over 15 years of experience in teaching at different Engineering colleges and tutoring across different boards including CBSE, ICSE, IGCSE, IBDP, Level AS/A in Mathematics & Science. Approachable to students & succeeded to boost their fundamental knowledge.
I used to struggle a lot with mathematics, but my tuition teacher has helped me improve tremendously. She explains concepts clearly and patiently, making even difficult topics easier to understand. Instead of simply giving answers, she encourages me to think independently and solve problems on my own, which has greatly improved my confidence and problem-solving skills. She provides plenty of practice and ensures that I fully understand each concept before moving on. Lessons with her are always engaging, enjoyable, and easy to follow. Most importantly, she understands my learning style and supports me whenever I face challenges. I am very grateful for her guidance and dedication.
Super Tutor
Shahdara Chitrakoot, Delhi
10 yrs of
Exp
74 students
4020 hrs of classes completed
650
per hour
Online Classes
With extensive experience in providing Class 10 tuition, I specialize in teaching mathematics, science, and computer science. My approach emphasizes a thorough understanding of key concepts and practical applications. In mathematics, I cover topics such as algebra, geometry, and trigonometry. My science classes include physics, chemistry, and biology, focusing on fundamental principles and real-world relevance. In computer science, I teach programming basics, algorithms, and data management. I use interactive tools, clear presentations, and regular assessments to ensure comprehensive learning. My goal is to build strong foundational knowledge, boost confidence, and prepare students for their board exams and future academic pursuits.
I’m really glad I found Rahul sir through UrbanPro. He has been extremely helpful with my Computer studies and has made understanding different concepts so much easier for me. He is very patient while explaining things and always makes sure that I actually understand the topic instead of just memorising it. I started taking his help after my Unit Tests, and it has genuinely made a big difference. With my half-yearlies coming up, I feel much more prepared and confident in Computer, and a lot of that is because of his guidance and support. He has helped me improve so much and has always been really supportive whenever I’ve had doubts. I’m really thankful for all his help and would definitely recommend him to anyone looking for a Computer tutor!
Top Tutor
Sector - 106, Noida
7 yrs of
Exp
18 students
2128 hrs of classes completed
350
per hour
Online Classes
I am a dedicated mathematics tutor with seven years of experience teaching students from grades 8 to 10 across IB, IGCSE, ICSE, and CBSE boards. I understand that many students struggle with math due to fear, lack of conceptual clarity, or difficulty in applying formulas. My approach focuses on simplifying complex concepts through real-life examples, step-by-step problem-solving, and interactive techniques to make learning engaging. I emphasize building a strong foundation and boosting students' confidence, ensuring they not only understand math but also enjoy it as a subject. I have found that students sometimes lack skills and sometimes they are not very well focused , so I can easily point these out
Top Tutor
Govindpuri Shiva Colony, Jaipur
10 yrs of
Exp
23 students
1478 hrs of classes completed
500
per hour
Online Classes
Tutor's home
I am a teacher of mathematics. I am giving online tuitions and tuitions at my home in Jaipur(Rajasthan). I have done M.Sc. , B.Ed. in mathematics. I have experience of 10 years of teaching mathematics , Vedic Mathematics and Olymiads.
I Shivani. N feel the class handled by Rohit Sir is a lively, interactive and also class room teaching experience with individual attention. I am looking forward to take weekly tests after which I will share my feed back on it. Thank you Sir.
Find more Tutor for Coordinate Geometry in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
