Perimeter and Area - Class 7 - Mathematics
Renews every month. Cancel anytime
Your personal doubt-solving assistant
Chatterbot AI gives you 100% accurate answers to your questions in an instant.
Examples - Perimeter and Area | NCERT | Mathematics | Class 7
One of the sides and the corresponding height of a parallelogram are $4 \mathrm{~cm}$ and $3 \mathrm{~cm}$, respectively. Find the area of the parallelogram (Fig 9.8 A parallelogram, its length as 4 cm, a perpendicular line upward and this height as 3 cm).
To find the area of a parallelogram, you can use the formula:
$$ \text{Area} = \text{base} \times \text{height} $$
Given the base $b = 4 , \mathrm{cm}$ and the height $h = 3 , \mathrm{cm}$, substituting these values into the formula gives:
$$ \text{Area} = 4 , \mathrm{cm} \times 3 , \mathrm{cm} = 12 , \mathrm{cm}^2 $$
Therefore, the area of the parallelogram is $12 , \mathrm{cm}^2$.
Find the height ' $x$ ' if the area of the parallelogram is $24 \mathrm{~cm}^{2}$ and the base is $4 \mathrm{~cm}$.
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowThe two sides of the parallelogram $\mathrm{ABCD}$ are $6 \mathrm{~cm}$ and $4 \mathrm{~cm}$. The height corresponding to the base $\mathrm{CD}$ is $3 \mathrm{~cm}$ (Fig 9.10). Find the
(i) area of the parallelogram.
(ii) the height corresponding to the base $\mathrm{AD}$.
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowFind the area of the following triangles (Fig 9.11).
Fig 9.11 contains two figures, both triangles, with some sides and heights labelled.
For figure (I):
A triangle $\triangle \mathrm{~PQR}$, with base $QR$ as $4 \mathrm{cm}$ long, and height $PS$ as $2 \mathrm{cm}$ long
For figure (ii):
A triangle $\triangle LMN$, with base $MN$ as $3 \mathrm{cm}$ long, and height $LO$ as $2 \mathrm{cm}$ long
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowFind $\mathrm{BC}$, if the area of the triangle $\mathrm{ABC}$ is $36 \mathrm{~cm}^{2}$ and the height $A D$ is $3 \mathrm{~cm}$ (Fig 9.12).
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowWhat is the circumference of a circle of diameter $10 \mathrm{~cm}$ (Take $\pi=3.14$ )?
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowWhat is the circumference of a circular disc of radius $14 \mathrm{~cm}$ ?
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowThe radius of a circular pipe is $10 \mathrm{~cm}$. What length of a tape is required to wrap once around the pipe $(\pi=3.14)$ ?
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowFind the perimeter of the given shape (Fig 9.23) (Take $\pi=\frac{22}{7}$ ).
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowSudhanshu divides a circular disc of radius $7 \mathrm{~cm}$ in two equal parts. What is the perimeter of each semicircular shape disc? (Use $\pi=\frac{22}{7}$ )
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowFind the area of a circle of radius $30 \mathrm{~cm}$ (use $\pi=3.14$ ).
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowThe diameter of a circular garden is $9.8 \mathrm{~m}$. Find its area.
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowThe adjoining figure shows two circles with the same centre. The radius of the larger circle is $10 \mathrm{~cm}$ and the radius of the smaller circle is $4 \mathrm{~cm}$.
Find: (a) the area of the larger circle
(b) the area of the smaller circle
(c) the shaded area between the two circles. $(\pi=3.14)$
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowExercise 9.1 - Perimeter and Area | NCERT | Mathematics | Class 7
Find the area of each of the following parallelograms
(I) The parallelogram has a base that is labelled as 7 cm.
The height (or altitude) drawn from the top vertex perpendicular to the base is labelled as 4 cm.
(ii) The parallelogram has a base that is labelled as 5 cm.
The height (or altitude) drawn from the top vertex perpendicular to the base is labelled as 3 cm.
(iii) The parallelogram has a base that is labelled as 2.5 cm.
The height (or altitude) drawn from the top vertex perpendicular to the base is labelled as 3.5 cm.
(iv) The parallelogram has a base that is labelled as 5 cm.
The height (or altitude) drawn from the top vertex perpendicular to the base is labelled as 4.8 cm.
(v) The parallelogram has a base that is labelled as 2 cm.
The height (or altitude) drawn from the top vertex perpendicular to the base is labelled as 4.5 cm.
The formula to calculate the area of a parallelogram is given by: $$\text{Area} = \text{Base} \times \text{Height}$$ where the base is the length of one of the parallelogram's sides and the height (or altitude) is the perpendicular distance from this base to the opposite side.
Let's calculate the area of each parallelogram based on this formula:
(I) Base = 7 cm, Height = 4 cm
Area = Base × Height = 7 cm × 4 cm = 28 cm²
(ii) Base = 5 cm, Height = 3 cm
Area = Base × Height = 5 cm × 3 cm = 15 cm²
(iii) Base = 2.5 cm, Height = 3.5 cm
Area = Base × Height = 2.5 cm × 3.5 cm = 8.75 cm²
(iv) Base = 5 cm, Height = 4.8 cm
Area = Base × Height = 5 cm × 4.8 cm = 24 cm²
(v) Base = 2 cm, Height = 4.5 cm
Area = Base × Height = 2 cm × 4.5 cm = 9 cm²
Thus, the areas of the parallelograms are:
For (I): 28 cm²
For (ii): 15 cm²
For (iii): 8.75 cm²
For (iv): 24 cm²
For (v): 9 cm²
Find the area of each of the following triangles
(I) The Triangle has a base that is labelled as 4 cm.
The height (or altitude) drawn from the top vertex perpendicular to the base is labelled as 3 cm.
(ii) The Triangle has a base that is labelled as 5 cm.
The height (or altitude) drawn from the top vertex perpendicular to the base is labelled as 3.2 cm.
(iii) The Triangle has a base that is labelled as 3 cm.
The height (or altitude) drawn from the top vertex perpendicular to the base is labelled as 4 cm.
(iv) The Triangle has a base that is labelled as 3 cm.
The height (or altitude) drawn from the top vertex perpendicular to the base is labelled as 2 cm.
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowFind the missing values:
S.No | Base | Height | Area of the Parallelogram |
---|---|---|---|
a. | $20 \mathrm{~cm}$ | $246 \mathrm{~cm}^{2}$ | |
b. | $15 \mathrm{~cm}$ | $154.5 \mathrm{~cm}^{2}$ | |
c. | $8.4 \mathrm{~cm}$ | $48.72 \mathrm{~cm}^{2}$ | |
d. | $15.6 \mathrm{~cm}$ | $16.38 \mathrm{~cm}^{2}$ |
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowFind the missing values:
Base | Height | Area of Triangle |
---|---|---|
$15 \mathrm{~cm}$ | $87 \mathrm{~cm}^{2}$ | |
$31.4 \mathrm{~mm}$ | $1256 \mathrm{~mm}^{2}$ | |
$22 \mathrm{~cm}$ | $170.5 \mathrm{~cm}^{2}$ |
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up now$\mathrm{PQRS}$ is a parallelogram (Fig 9.14). QM is the height from Q to SR and QN is the height from Q to $P S$. If $S R=12 \mathrm{~cm}$ and $Q M=7.6 \mathrm{~cm}$. Find:
(a) the area of the parallegram $\mathrm{PQRS}$
(b) $\mathrm{QN}$, if $\mathrm{PS}=8 \mathrm{~cm}$
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up now$\mathrm{DL}$ and $\mathrm{BM}$ are the heights on sides $\mathrm{AB}$ and $\mathrm{AD}$ respectively of parallelogram $\mathrm{ABCD}$ (Fig 9.15). If Fig 9.15 the area of the parallelogram is $1470 \mathrm{~cm}^{2}, \mathrm{AB}=35 \mathrm{~cm}$ and $\mathrm{AD}=$ $49 \mathrm{~cm}$, find the length of BM and DL.
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up now$\triangle \mathrm{ABC}$ is right angled at $\mathrm{A}$ (Fig 9.16). $\mathrm{AD}$ is perpendicular to $\mathrm{BC}$. If $\mathrm{AB}=5 \mathrm{~cm}$, $B C=13 \mathrm{~cm}$ and $A C=12 \mathrm{~cm}$, Find the area of $\triangle A B C$. Also find the length of $\mathrm{AD}$.
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up now$\triangle \mathrm{ABC}$ is isosceles with $\mathrm{AB}=\mathrm{AC}=7.5 \mathrm{~cm}$ and $\mathrm{BC}=9 \mathrm{~cm}$ (Fig 9.17). The height $A D$ from $A$ to $B C$, is $6 \mathrm{~cm}$. Find the area of $\triangle A B C$. What will be the height from $C$ to $\mathrm{AB}$ i.e., $\mathrm{CE}$ ?
Here, $CE$ is perpendicular to $AB$
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowExercise 9.2 - Perimeter and Area | NCERT | Mathematics | Class 7
Find the circumference of the circles with the following radius: (Take $\pi=\frac{22}{7}$ ) with steps
(a) $14 \mathrm{~cm}$
(b) $28 \mathrm{~mm}$
(c) $21 \mathrm{~cm}$
To find the circumference of a circle given its radius $r$, we use the formula: $$C = 2\pi r$$ where $\pi = \frac{22}{7}$ for these problems.
Steps for each part:
(a) For radius $14 , \mathrm{cm}$:
Substitute $r = 14 , \mathrm{cm}$ into the formula.
$C = 2 \times \frac{22}{7} \times 14$
Simplify the expression.
$C = 2 \times 22 \times 2$
Calculate the value.
(b) For radius $28 , \mathrm{mm}$:
Substitute $r = 28 , \mathrm{mm}$ into the formula.
$C = 2 \times \frac{22}{7} \times 28$
Simplify the expression.
$C = 8 \times 22$
Calculate the value.
(c) For radius $21 , \mathrm{cm}$:
Substitute $r = 21 , \mathrm{cm}$ into the formula.
$C = 2 \times \frac{22}{7} \times 21$
Simplify the expression.
$C = 6 \times 22$
Calculate the value.
Let's carry out the simplified calculations next. Here are the results for the circumferences of the circles:
(a) For a radius of $14 , \mathrm{cm}$, the circumference is $88 , \mathrm{cm}$.
(b) For a radius of $28 , \mathrm{mm}$, the circumference is $176 , \mathrm{mm}$.
(c) For a radius of $21 , \mathrm{cm}$, the circumference is $132 , \mathrm{cm}$.
Find the area of the following circles, given that:
(a) radius $=14 \mathrm{~mm}$ (Take $\pi=\frac{22}{7}$ )
(b) diameter $=49 \mathrm{~m}$
(c) radius $=5 \mathrm{~cm}$
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowIf the circumference of a circular sheet is $154 \mathrm{~m}$, find its radius. Also find the area of the sheet. (Take $\pi=\frac{22}{7}$ ) with steps
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowA gardener wants to fence a circular garden of diameter $21 \mathrm{~m}$. Find the length of the rope he needs to purchase, if he makes 2 rounds of fence. Also find the cost of the rope, if it costs ₹ 4 per meter. (Take $\pi=\frac{22}{7}$ ) with steps
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowFrom a circular sheet of radius $4 \mathrm{~cm}$, a circle of radius $3 \mathrm{~cm}$ is removed. Find the area of the remaining sheet. (Take $\pi=3.14$ ) with steps
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowSaima wants to put a lace on the edge of a circular table cover of diameter $1.5 \mathrm{~m}$. Find the length of the lace required and also find its cost if one meter of the lace costs ## ₹ 15. (Take $\pi=3.14$ )
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowFind the perimeter of the adjoining figure, which is a semicircle including its diameter which is 10 cm with steps
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowFind the cost of polishing a circular table-top of diameter $1.6 \mathrm{~m}$, if the rate of polishing is ₹ $15 / \mathrm{m}^{2}$. (Take $\pi=3.14$ )
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowShazli took a wire of length $44 \mathrm{~cm}$ and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take $\pi=\frac{22}{7}$ )
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowFrom a circular card sheet of radius $14 \mathrm{~cm}$, two circles of radius $3.5 \mathrm{~cm}$ and a rectangle of length $3 \mathrm{~cm}$ and breadth $1 \mathrm{~cm}$ are removed. (as shown in the adjoining figure). Find the area of the remaining sheet. (Take $\pi=\frac{22}{7}$ )
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowA circle of radius $2 \mathrm{~cm}$ is cut out from a square piece of an aluminium sheet of side $6 \mathrm{~cm}$. What is the area of the left over aluminium sheet? (Take $\pi=3.14$ )
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowThe circumference of a circle is $31.4 \mathrm{~cm}$. Find the radius and the area of the circle? (Take $\pi=3.14$ )
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowA circular flower bed is surrounded by a path $4 \mathrm{~m}$ wide. The diameter of the flower bed is $66 \mathrm{~m}$. What is the area of this path? $(\pi=3.14)$
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowA circular flower garden has an area of $314 \mathrm{~m}^{2}$. A sprinkler at the centre of the garden can cover an area that has a radius of $12 \mathrm{~m}$. Will the sprinkler water the entire garden? (Take $\pi=3.14$ )
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowFind the circumference of the inner and the outer circles, shown in the adjoining figure? (Take $\pi=3.14$ ) Radius of the inner circle is 9m and outer circle is 10 m.
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowHow many times a wheel of radius $28 \mathrm{~cm}$ must rotate to go $352 \mathrm{~m}$ ? (Take $\pi=\frac{22}{7}$ )
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowThe minute hand of a circular clock is $15 \mathrm{~cm}$ long. How far does the tip of the minute hand move in 1 hour. (Take $\pi=3.14$ )
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowExtra Questions - Perimeter and Area | NCERT | Mathematics | Class 7
Area of a circle is $36$ $cm^2$ and the area of a rectangle is $\frac{1}{6}$ of the area of the circle. If the breadth of the rectangle is $1$ cm, find its length?
A) $6$ cm
B) $12$ cm
C) $36$ cm
D) $26$ cm
Solution:
The area of the rectangle is given by:
$$ \text{Area of rectangle} = \frac{1}{6} \times \text{Area of circle} $$
Given that the Area of the circle is $36 \, \text{cm}^2$, we can calculate:
$$ \text{Area of rectangle} = \frac{1}{6} \times 36 \, \text{cm}^2 = 6 \, \text{cm}^2 $$
Also, the rectangle's area can be expressed in terms of its dimensions:
$$ \text{Area of rectangle} = \text{length} \times \text{breadth} $$
With a breadth of $1 \, \text{cm}$, it follows:
$$ \text{Area of rectangle} = \text{length} \times 1 \, \text{cm} = 6 \, \text{cm}^2 $$
Thus:
$$ \text{length} = 6 \, \text{cm} $$
Therefore, the length of the rectangle is 6 cm, which corresponds to option A).
In the newspaper, you read about a football match between Brazil and Turkey. The countries were represented with their respective flags. You noticed a similar shape on Brazil's flag as kaju barfi. The length of the base of that shape is $10.6 \mathrm{~m}$ and the height is equal to $8.3 \mathrm{~m}$. So, the area of the yellow parallelogram in the flag is
A. $87 \mathrm{~m}^{2}$
B. $88 \mathrm{~m}^{2}$
C. $86 \mathrm{~m}^{2}$
D. $78 \mathrm{~m}^{2}$
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowImprove your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowImprove your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowImprove your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowImprove your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowImprove your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowImprove your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowImprove your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowIf a wire is stretched, what happens - does the length of the wire increase or the area of the wire decrease?
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowImprove your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowImprove your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowImprove your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up now