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Q1(d):
Find the area of each of the following parallelograms:
(d) 
Find the area of each of the following parallelograms:
(d)
Solution :
Given Variables & Initial Setup
Based on the standard geometric parameters provided in the referenced figure (d), we extract the following dimensions for the parallelogram:
- Base ($b$): $5 \text{ cm}$
- Corresponding Height ($h$): $4.8 \text{ cm}$
The height represents the perpendicular distance between the chosen base and its opposite parallel side.
Geometric Visualization
Below is the geometrically accurate representation of the parallelogram. The base is scaled to $200$ units and the height to $192$ units, preserving the exact mathematical ratio of $5 : 4.8$.
Step 1: Stating the Governing Geometric Formula
The area of a parallelogram is defined as the total two-dimensional space enclosed within its four sides. [Per Euclidean Geometry], any 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 $A$ is the product of its base and its corresponding perpendicular height:
$A = \text{Base} \times \text{Height}$
$A = b \times h$
Step 2: Substituting the Given Values
Substitute the extracted dimensions into the area formula. Ensure that both measurements are in the same units (centimeters) to yield an area in square centimeters ($\text{cm}^2$).
$A = 5 \text{ cm} \times 4.8 \text{ cm}$
Step 3: Executing the Arithmetic Calculation
To multiply $5$ by $4.8$, we can use the distributive property or convert the decimal to a fraction for absolute precision:
$A = 5 \times \left( \frac{48}{10} \right)$
$A = \frac{5 \times 48}{10}$
$A = \frac{240}{10}$
$A = 24$
Final Solution: The area of the parallelogram is $24 \text{ cm}^2$.
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(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(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
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