Find the best tutors and institutes for Class 10 Tuition
Q3(a):
Find the missing values: Base = $20$ cm, Height = ______, Area of the Parallelogram = $246$ cm$^2$.
Solution :
Initial Setup & Given Variables
We are tasked with determining the missing dimension of a parallelogram given its area and base. Let us define the known scalar quantities:
- Base ($b$) = $20 \text{ cm}$
- Area ($A$) = $246 \text{ cm}^2$
- Height ($h$) = Unknown
Theoretical Foundation
The area of a parallelogram is defined as the region enclosed by its four sides in a two-dimensional plane. [Per the standard geometric theorem for the area of a parallelogram], the area is equal to the product of its base and the corresponding perpendicular height. The formula is expressed as:
$A = b \times h$
Where:
- $A$ represents the total area.
- $b$ represents the length of the base.
- $h$ represents the perpendicular height (altitude) drawn to that base.
Geometric Visualization
Below is a precise, scaled vector representation of the parallelogram, illustrating the relationship between the base, the perpendicular height, and the total enclosed area.
Step 1: Setting up the Equation
By substituting the given values into the area formula, we establish a linear equation with one variable ($h$).
$246 = 20 \times h$
Step 2: Algebraic Manipulation
To isolate the variable $h$, we apply the Division Property of Equality. We divide both sides of the equation by the coefficient of $h$, which is $20$.
$h = \frac{246}{20}$
Step 3: Calculation and Simplification
We perform the division to find the exact decimal value of the height. We can simplify the fraction by dividing the numerator and the denominator by $2$ first:
$h = \frac{123}{10}$
Dividing by $10$ shifts the decimal point one place to the left:
$h = 12.3 \text{ cm}$
Final Solution: The missing height of the parallelogram is $12.3 \text{ cm}$.
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(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(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 $PQRS$.
- 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
I have volunteer teacher for evidyaloka ..I thought higg school students math and science
Private teacher. Classes will be taken for science also but only for Physics and Chemistry. I have been teaching for Class 10 for the past 15 years. Focus will be given to each student regarding their difficult concepts. Previous year question papers will be discussed, along with practice worksheets that will be given for each chapter. Coaching will be given to score good marks in respective board exams by giving them tricks to manage the timings
Wonderful teacher with enormous knowledge about the subject with a smile every time while teaching...
I have motivated many 10th std student who scored more than 85% I love teaching and I can make you understand what actually studies is!!! It's all about practise and applications
I highly recommend Shivam Sir for Class 10 Mathematics and Science. He taught my brother, and the improvement in his understanding and confidence was remarkable. Before joining his classes, my brother found several concepts difficult, but Shivam Sir explained every topic in a very simple, practical, and easy-to-understand manner. He always ensured that every concept was clear before moving on to the next chapter. His teaching style is interactive and student-friendly. He patiently answers every doubt, gives plenty of practice questions, conducts regular tests, and provides useful tips for board exams. He also shares short tricks, revision strategies, and focuses on strengthening concepts rather than just memorizing answers.
22 Years Experience in Schools IN ICSE/CBSE/IGCSE IN DIFFERENT STATE BOARDS
Sir is very friendly teacher he will support us more he is the best teacher of the year his teaching skills are really good.
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
Download free CBSE - Class 9 Mathematics Coordinate Geometry EXERCISE 9.1 worksheets
Download Now