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Q1(e):
Find the area of each of the following parallelograms:
(e) 
Find the area of each of the following parallelograms:
(e)
Solution :
Step 1: Given Variables & Initial Setup
Based on the standard geometric parameters provided in the referenced figure for this specific problem, we extract the following dimensions for the parallelogram:
- Base ($b$): $2\text{ cm}$
- Corresponding Height/Altitude ($h$): $4.4\text{ cm}$
[Note: In a parallelogram, any of the four sides can be chosen as the base. The corresponding height is the perpendicular distance from the chosen base to the opposite parallel side.]
Step 2: Geometric Visualization
Below is a mathematically scaled, high-precision vector representation of the parallelogram, illustrating the relationship between the base and its corresponding altitude.
Step 3: Mathematical Formulation
By the fundamental axioms of Euclidean geometry, a parallelogram can be transformed into a rectangle of equal area by translating the right-angled triangle formed by the altitude to the opposite side. Therefore, the area ($A$) of a parallelogram is strictly defined as the product of its base and its corresponding height.
The governing formula is:
$\text{Area} = \text{Base} \times \text{Height}$
$A = b \times h$
Step 4: Execution & Algebraic Calculation
Substitute the given scalar values into the area formula:
$A = 2\text{ cm} \times 4.4\text{ cm}$
To ensure absolute precision, we can perform the multiplication by converting the decimal to a fraction [Per standard arithmetic operations]:
$A = 2 \times \left(\frac{44}{10}\right)$
$A = \frac{88}{10}$
$A = 8.8$
Step 5: Dimensional Analysis
We must verify the units of the final result. Multiplying a one-dimensional length by another one-dimensional length yields a two-dimensional area:
$[\text{cm}] \times [\text{cm}] = [\text{cm}^2]$
The magnitude is $8.8$ and the unit is $\text{cm}^2$. The calculation is dimensionally consistent and mathematically sound.
Final Solution: The area of the parallelogram is $8.8\text{ cm}^2$.
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)
- 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(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
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