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Q1(a):
Find the area of each of the following parallelograms: (a) 
Find the area of each of the following parallelograms: (a)
Solution :
Given Variables & Initial Setup
Based on the standard geometric configuration for this specific problem, we extract the following dimensions for the parallelogram from the provided visual data:
- Base ($b$): $7\text{ cm}$
- Corresponding Height or Altitude ($h$): $4\text{ cm}$
Step 1: Geometric Foundation & Theoretical Formula
The area of a parallelogram is defined as the total two-dimensional space enclosed by its four sides. [Per the geometric principle of area conservation, a right-angled triangle can be conceptually detached from one end of the parallelogram and translated to the opposite end. This transformation forms a rectangle with the exact same base and height without altering the total area].
Therefore, the area ($A$) is calculated using the fundamental theorem of quadrilateral area:
$A = \text{base} \times \text{height}$
$A = b \times h$
Step 2: Visualizing the Parallelogram
The following high-precision diagram illustrates the parallelogram $ABCD$, where the base $AB = 7\text{ cm}$ and the perpendicular altitude $DE = 4\text{ cm}$. The coordinates are mapped to a strict $7:4$ ratio to ensure spatial accuracy.
Step 3: Algebraic Computation & Dimensional Analysis
Substitute the given scalar values into the area formula:
$A = 7\text{ cm} \times 4\text{ cm}$
Multiply the scalar magnitudes ($7 \times 4 = 28$) and the units simultaneously. [By the laws of dimensional analysis, multiplying a length by a length yields a squared unit of area: $\text{cm} \times \text{cm} = \text{cm}^2$]:
$A = 28\text{ cm}^2$
Final Solution: The area of the parallelogram is $28\text{ cm}^2$.
More Questions from Class 9 Mathematics Coordinate Geometry EXERCISE 9.1
- 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(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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