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CBSE Questions for Class 7 Maths Perimeter And Area Quiz 11 - MCQExams.com
CBSE
Class 7 Maths
Perimeter And Area
Quiz 11
An increase in perimeter of a figure always increases the area of the figure.
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0%
True
0%
False
Explanation
It is false.
It is not necessary, bemuse the perimeter is the sum of all sides of closed shapes or polygons while the area is just bounded space insides.
Suppose we make hole in a circle then its perimeter will increase because now there is one more edge(circumference) in new shape, but area will decrease because there is less area available compare to original shape.
Hence, given statement is false.
In given Fig. ratio of the area of triangle ABC to the area of triangle ACD is the same as the ratio of base BC of triangle ABC to the base CD of triangle ACD.
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0%
True
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False
Explanation
It is true.
In $$\Delta ABC$$ $$BC$$ is base and $$AC$$ is height
So, Area $$(\Delta ABC) = \dfrac {1}{2} \times BC \times AC $$
Also, In $$\Delta ACD$$ $$CD$$ is base and $$AC$$ is height
So, Area $$(\Delta ACD) = \dfrac {1}{2} \times CD \times AC $$
$$\therefore \cfrac{\text{Area }(\Delta ABC)}{\text{Area }(\Delta ACD)}=\cfrac{\dfrac {1}{2} \times BC \times AC}{\dfrac {1}{2} \times CD \times AC}=\cfrac{BC}{CD}$$
$$5$$ hectare $$= 500\, m^2$$
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0%
True
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False
Explanation
It is false.
Because, we know that,
$$\Rightarrow 1 \text{ hectare} =10000 \ m^2$$
$$\Rightarrow 5\text{ hectare}=5\times 10000 \,m^2 =50000 \,m^2$$.
The area of a parallelogram is 60 $$cm^2$$ and one of its altitude is 5 cm. The length of its corresponding side is
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12 cm
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6 cm
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4 cm
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2 cm
Explanation
Area of a parallelogram =
$$ side \times altitude$$
$$ \Rightarrow a \times h $$ = 60
$$ \Rightarrow a \times 5 $$ = 60
$$ \Rightarrow a= \dfrac{60}{5} $$
$$ \Rightarrow a=12 cm $$
In covering a distance s meters, a circular wheel of radius $$ r $$m makes $$\dfrac{s}{2\pi r}$$ revolutions. Is the statement true ? Why ?
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0%
True
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False
Explanation
Distance covered by a circular wheel in a revolution $$= 2 \pi r n$$
where $$n =$$ number of revolutions
$$\therefore s = 2 \pi rn$$ or $$n = \dfrac{S}{2\pi r}$$
Hence, verifies the given statement true.
Is it true that the distance travelled by circular wheel of diameter d cm is one revolution is $$2\pi d \,cm$$ ? Why ?
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0%
True
0%
False
Explanation
Distance travelled by wheel in one revolution is equal to the circumference of wheel
$$= 2\pi r = \pi(2r) = \pi d.\neq2\pi d$$
Hence, the given statement is false.
Is the area of the largest circle that can be drawn inside a rectangle of length $$a$$ cm and breadth $$b$$ cm $$(a > b)$$ is $$\pi b^2 \,cm^2$$ ? Why ?
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0%
True
0%
False
Explanation
The diameter of circle that can be drawn inside the rectangle is equal to the breadth of rectangle.
The length of the rectangle $$= a \,\,cm$$
The breadth of the rectangle $$= b \,\,cm$$
$$\therefore$$ Diameter of circle $$= b \,\,cm$$
$$\Rightarrow r = \dfrac{b}{2} \,cm$$
$$\therefore$$ Area of circle $$A = \pi r^2 = \pi \left ( \dfrac{b}{2} \right )^2 = \dfrac{1}{4} \pi b^2 \,cm^2$$
Hence, the given statement is false.
Find the area of a ring-shaped region enclosed between two concentric circles of diameter $$8cm$$ and $$6cm$$
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$$28\ cm^2$$
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$$44\ cm^2$$
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$$66\ cm^2$$
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$$88\ cm^2$$
Explanation
We know that area of a circle is $$πr^2$$, where $$r$$ be a radius of the circle.
Let us assume $$R = 8$$ $$cm$$ & $$r = 6$$ $$cm$$
$$\therefore$$ Required area $$= \pi (R^2 - r^2 ) = \pi (8^{2} - 6^{2}) = 28π \ cm^{2}$$.
The area of circle whose circumference is $$44cm$$ is
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$$77\ cm^2$$
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$$308\ cm^2$$
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$$168\ cm^2$$
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$$154\ cm^2$$
Explanation
Let $$C$$ is circumference of circle
Given $$C=44\quad cm$$
$$\therefore 2\pi r=44$$
$$\therefore 2\times \frac { 22 }{ 7 } \times r=44$$
$$\therefore r=\frac { 44\times 7 }{ 44 } $$
$$\therefore r=7\quad cm$$
Thus, radius of circle is 7 cm.
Now, Area of circle is given by,
$$A=\pi { r }^{ 2 }$$
$$\therefore A=\frac { 22 }{ 7 } \times { 7 }^{ 2 }$$
$$\therefore A=22\times 7$$
$$\therefore A=154\quad { cm }^{ 2 }$$
Thus, area of circle is $$154\quad { cm }^{ 2 }$$
The external and internal radius of a circle path area $$5 m$$ and $$3m$$ respectively. The are of the circular path is
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$$87 \pi m^2$$
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$$16 \pi m^2$$
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$$157 \pi m^2$$
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$$237 \pi m^2$$
Explanation
We know that area of a circle is $$πr^2$$, where $$r$$ be a radius of the circle.
Let us assume $$R = 5$$ $$m$$ & $$r = 3$$ $$m$$
$$\therefore$$ Required area $$= \pi (R^2 - r^2 ) = \pi (5^{2} - 3^{2}) = 16π \ m^{2}$$.
The radius of a circle is $$5\ cm$$ then its area is
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$$154\ cm^2$$
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$$1386\ cm^2$$
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$$550\ cm^2$$
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$$308\ cm^2$$
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None
Explanation
Area of circle $$=$$ $${\pi r}^2$$
$$=3.14\times5\times5$$
$$=78.5\ cm^2$$
Hence, option $$E$$ is correct.
If $$\pi=\dfrac{22}{7}$$
then distance covered in the revolution (in m) of a wheel of diameter $$35cm$$willbe
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$$2.2$$
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$$1.1$$
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$$9.625$$
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$$96.25$$
Explanation
Diameter of wheel$$= 35\,cm$$
∴ Radius of wheel (r)$$=\dfrac{35}{2}\,cm$$
Distance covered in $$1$$ revolution by wheel = circumference of wheel
$$= 2\pi r$$
$$= 2 \times \dfrac{22}{7} \times \dfrac{35}{2}$$
$$= 110\,cm =1.1\,m$$
Thus, option (B) is correct.
The area between two concentric circles will be :
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$$\pi R^2$$
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$$\pi (R^2 - r ^2)$$
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$$\pi(R^2-r)$$
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None of these
Explanation
Area of $$C_1=\pi R^2$$
Area of $$C_2=\pi r^2$$
The area between two concentric circles$$= \pi R^2 – \pi r^2$$
$$= \pi(R^2 - r^2)$$
Thus, option (B) is correct.
The area of a right-angled triangle is 36 sq. cm and its base 9 cm, then the length of perpendicular will be:
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$$8\,cm$$
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$$4\,cm$$
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$$16\,cm$$
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$$32\,cm$$
Explanation
Area of right angled triangle $$=\dfrac{1}{2}\times base \times height$$
$$36=\dfrac{1}{2}\times 9\times h$$
$$h=\dfrac{72}{9}$$
$$h=8\,cm$$
Sabhia wants to colour the top of her geometry box which is in the shape of rectangle of length $$7$$ $$cm$$ and breadth $$4$$ $$cm$$. If the cost of colouring $$1$$ $$cm^2$$ is $$Rs.$$ $$10$$, then find the total amount that she has to pay for colouring.
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$$Rs.$$ $$250$$
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$$Rs.$$ $$260$$
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$$Rs.$$ $$270$$
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$$Rs.$$ $$280$$
The area of square of side $$4$$ $$m$$ is ____ and the cost of land is _____, if $$1$$ $$m^2$$ costs $$Rs.$$ $$1000.$$
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$$14$$ $$m^2$$, $$Rs.$$ $$16,000$$
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$$16$$ $$m^2$$, $$Rs.$$ $$16,000$$
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$$14$$ $$m^2$$, $$Rs.$$ $$14,000$$
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$$16$$ $$m^2$$, $$Rs.$$ $$14,000$$
It is given that side of a square is same as the length of rectangle. Also, the square and the rectangle both have same area, then we can conclude that
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breadth of the rectangle $$=$$ side of the square
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breadth of the rectangle $$\neq$$ side of the square
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can't say anything
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none of these
What is the area of shape? Each square in the grid is $$2 \times 2 $$ unit square. Also find the cost of obtained area, if one square in the grid costs $$Rs.$$ $$100$$.
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$$42$$ unit square, $$Rs.$$ $$4200$$
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$$42$$ unit square, $$Rs.$$ $$44000$$
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$$44$$ unit square, $$Rs.$$ $$4400$$
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$$44$$ unit square, $$Rs.$$ $$44000$$
What will be cost to fence a rectangular park of length $$20$$ meter and breadth $$12$$ meter at the rate of $$25$$ rupees per meter.?
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$$Rs.$$ $$1590$$
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$$Rs.$$ $$1690$$
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$$Rs.$$ $$1500$$
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$$Rs.$$ $$1600$$
On the basis of given figure, can we say that both the triangles $$T1$$ and $$T2$$ have same area?
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Yes
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No
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Can't say anything
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None of these
Observe the given figure, then find the missing value in the following:
Area of triangle $$ABC = \dfrac{1}{2} \times AB \times BC = \dfrac{1}{2} \times BC \times ?$$
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$$AC$$
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$$AB$$
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$$BC$$
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None of these
Sonali wants to do fencing around a rectangular garden of length $$20$$ and breadth $$12$$. If the cost of fencing is $$12$$ rupees per $$m$$, then find the total cost of fencing for the entire garden.
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$$Rs.$$ $$700$$
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$$Rs.$$ $$750$$
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$$Rs.$$ $$7600$$
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$$Rs.$$ $$768$$
Observe the given figure and hence choose the correct answer: Rectangle with area $$A_1$$ has been divided into two triangles of area $$A_2$$ and $$A_3$$
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Area of $$A1 \neq $$ area of $$A2$$
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Area of $$A1$$ $$=$$ area of $$A2 + $$ area of $$A3$$
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Area of $$A1 = $$ area of $$A3$$
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Area of $$A1 =2 \times $$ area of $$A2 = 2 \times $$ area of $$A3$$
Fill in the blank:
Area of the right angle triangle is half the _______ of the lengths of its legs.
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sum
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product
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division
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none of these
It is given that both the triangles $$ABC$$ and $$PQR$$ as shown in figure have same area and is equals to $$24$$ square units. Can we say that both the triangles are congruent?
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Yes
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No
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Can't say anything
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None of these
The length and breadth of a rectangular field are equal to $$60$$ $$m$$ and $$40$$ $$m$$ respectively. Find the cost of the grass to be planted in it at the rate of $$Rs.$$ $$2.50$$ per $$m^2$$.
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$$Rs. $$ $$60$$
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$$Rs. $$ $$600$$
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$$Rs. $$ $$6000$$
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$$Rs. $$ $$60000$$
Any two isosceles triangles are of same area, then both are _____.
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always congruent
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never congruent
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may or may not be congurent
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none of these
Kartik wants to buy a pastel sheet for drawing, which is in the shape of a square of side $$6$$ $$cm$$. Then what amount he has to pay to the shopkeeper if the cost of $$1$$ $$cm^2$$ is $$Rs.$$ $$10$$?
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$$Rs.$$ $$600$$
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$$Rs.$$ $$620$$
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$$Rs.$$ $$700$$
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None of these
Lavisha has a handkerchief in a triangular shape as shown in the figure. The area of her handkerchief in $$m^2$$ is _____.
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$$0.54$$
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$$5.4$$
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$$54$$
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$$540$$
Fill in the blank:
$$2.34$$ $$m^2 = $$ ____ $$cm^2$$
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$$23.4$$
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$$234$$
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$$2340$$
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$$23400$$
Explanation
We know that $$1m^2 = (100 \times 100) cm^2 = 10000cm^2$$
We are given $$2.34m^2$$
Using the above mentioned conversion, we get
$$2.34m^2 = 2.34 \times 10000 = 23400cm^2 $$
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