2 Marks Questions

Question 12 Marks

Find the area of a square whose side is: $4.1\ cm$

Answer

Area of a square $= ($Side $\times $ Side$)$
Side of the square $= 4.1\ cm$
Area of the square $= (4.1 \times 4.1)$
$= 16.81\ cm^2$

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Question 22 Marks

Find the area of a square whose side is: $5\ cm$

Answer

Area of a square $= ($Side $\times $ Side$)$
Side of the square $=5\ cm$
Area of the square $= 5 \times 5 = 25\ cm^2$

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Question 32 Marks

Find the perimeter of the square whose side is given below: $5m$

Answer

Perimeter of a square $= 4 \times ($Length of one side$)$
Length of one side $= 5m$
Perimeter $= 4 \times 5 = 20m$

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Question 42 Marks

Split the following shape into rectangles and find the area. (The measures are given in centimeter.)

Answer

This figure consists of two rectangles $I$ and $II.$

The area of rectangle $I = ($Length $\times $ Breadth$)$
$= 10 \times 2$
$= 20\ cm^2$
Similarly, area of rectangle $II = ($Length $\times $ Breadth$)$
$= 10 \times 32$
$= 15\ cm^2$
Thus, total area of this figure $= ($Area of rectangle $I\ +$ Area of rectangle $II)$
$= 20 + 15$
$= 35\ cm^2$

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Question 52 Marks

Find the side of the square whose perimeter is: $40\ cm$

Answer

Side of a square $=$ Perimeter $4$ Perimeter $= 40\ cm$ Side of this square $=\frac{40}{4}$
$=4\text{cm}$

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Question 62 Marks

Find the perimeter of the rectangle whose lengths and breadths are given below: $7.5\ cm, 4.5\ cm$

Answer

Perimeter of a rectangle $= 2 \times ($Length $+$ Breadth$)$ Since,
Length $= 7.5\ cm,$
Breadth $= 4.5\ cm$
Therefore, Perimeter $= 2 \times (7.5 + 4.5) = 2 \times (12) = 24\ cm$

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Question 72 Marks

Find the side of the square whose perimeter is: $22\ cm$

Answer

Side of a square $=$ Perimeter $4$ Perimeter $= 22\ cm$
Side of this square $=\frac{22}{4}$
$=5.5\text{cm}$

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Question 82 Marks

Find the perimeter of the rectangle whose lengths and breadths are given below: $5\ cm, 4\ cm$

Answer

Perimeter of a rectangle $= 2 \times ($Length $+$ Breadth$)$
Since, Length $= 5\ cm,$
Breadth $= 4\ cm$
Therefore, Perimeter $= 2(5 + 4) = 2 \times (9) = 18\ cm$

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Question 92 Marks

Find the area of a rectangle, whose Length $= 4.5\ cm$, breadth $= 2\ cm$

Answer

Area of a rectangle $= ($Length $\times $ Breadth$)$
Length $= 4.5\ cm,$ Breadth $= 2\ cm$
Area of rectangle $= 4.5 \times 2$
$=9\ cm^2$

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Question 102 Marks

The following figure is drawn on a squared paper. Count the number of square enclosed by figure and find its area, taking the area of square as $1\ cm^2$.

Answer

There are $16$ complete squares in the given shape.
Since, Area of one square $= 1\ cm^2$
Therefore, Area of this shape $= 16 \times 1 = 16\ cm^2$

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Question 112 Marks

The following figure is drawn on a squared paper. Count the number of square enclosed by figure and find its area, taking the area of square as $1\ cm^2$.

Answer

There are $20$ complete and $ 8$ half squares in the given shape.
Since, Area of one square $= 1\ cm^2$
Therefore, Area of this shape $= (20 + 8 \times 12) = 24\ cm^2$

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Question 122 Marks

Find the area of a square whose side is: $5.5\ cm$

Answer

Area of a square $= ($Side $\times $ Side$)$
Side of the square $= 5.5\ cm$
Area of the square $= (5.5 \times 5.5)$
$ = 30.25\ cm^2$

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Question 132 Marks

Avneet buys $9$ square paving slabs, each with a side of $\frac{1}{212}\text{m}.$ He lays them in the form of a square.

$i.\ $What is the perimeter of his arrangement?

$ii.\ $Shari does not like his arrangement. She gets him to lay them out like a cross. What is the perimeter of her arrangement?

$iii.\ $Which has greater perimeter?

$iv.\ $Avneet wonders, If there is a way of getting an even greater perimeter. Can you find a way of doing this? $($The paving slabs must meet along complete edges they cannot be broken$)$

Answer

$i.\ $Length of the side of one slab $=\frac{1}{2}\text{m}$
In the square arrangement, one side of the square is formed by three slabs.
So, length of the side of the square $=3\times\frac{1}{2}=\frac{3}{2}\text{m}$
The perimeter of the square arrangement $=4\times\frac{3}{2}=6\text{m}$
$ii.\ $The cross arrangement consists of $8$ sides.
These sides form the periphery of the arrangement and measure $1m$ each.
Also, this arrangement consists of other $4$ sides that measure $\frac{1}{2}\text{m}$ each.
So, the perimeter of the cross arrangement$=\Big(1+\frac{1}{2}+1+1+\frac{1}{2}+1+1+\frac{1}{2}+1+1+\frac{1}{2}+1\Big)$
$=(8+2)=10\text{m}$

$iii.\ $Perimeter of the cross arrangement $= 10m$
Perimeter of the square arrangement $= 6m$
Thus, the perimeter of the cross arrangement is more than that of the square arrangement.
$iv.\ $No, there is no way of arranging these slabs where the perimeter is more than $10m.$

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Question 142 Marks

Find the area of a square whose side is: $2.6\ cm$

Answer

Area of a square $= ($Side $\times $ Side$)$
Side of the square $= 2.6\ cm$
Area of the square $= (2.6 \times 2.6)$
$ = 6.76\ cm^2$

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Question 152 Marks

The side of a square is $70\ cm.$ Find its area and perimeter.

Answer

Side of the square $= 70\ cm$
Area of the square $= ($Side $\times $ Side$)$
$= 70 \times 70$
$= 4900\ cm^2$
Perimeter of the square $= (4 \times $ Side$)$
$= 4 \times 70$
$= 280\ cm$

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Question 162 Marks

The following figure is drawn on a squared paper. Count the number of square enclosed by figure and find its area, taking the area of square as $1\ cm^2$.

Answer

There are $15$ complete and $6$ half squares in the given shape.
Since, Area of one square $= 1\ cm^2$
Therefore, Area of this shape $= (15 + 6 \times 12) = 18\ cm^2$

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Question 172 Marks

The area of a rectangle is $225\ cm^2$ and its one side is $25\ cm,$ find its other side.

Answer

Area $= 225\ cm^2$
One of the sides $= 25\ cm$
Area of the rectangle $=$ Product of the lengths of its two side
Other side $=\frac{\text{Area}}{\text{Side}}$
$=\frac{225}{25}$
$9\text{cm}$

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Question 182 Marks

Find the breadth of the rectangle whose perimeter is $360\ cm$ and whose length is:$116\ cm$

Answer

Perimeter of a rectangle $= 2($Length $+$ Breadth$)$
Therefore, Breadth of the rectangle $=\frac{\text{Perimeter}}{2}-\text{Length}$
Perimeter $= 360\ cm $
$$Length $= 116\ cm$
Breadth $=\frac{360}{2}-116$
$= 180 - 116 = 64\ cm$

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Question 192 Marks

The following figure is drawn on a squared paper. Count the number of square enclosed by figure and find its area, taking the area of square as $1\ cm^2$.

Answer

There are $36$ complete squares in the given shape.
Since, Area of one square $= 1\ cm^2$
Therefore, Area of $36$ squares $= 36 \times 1 = 36\ cm^2$

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Question 202 Marks

Find the perimeter of a regular hexagon with each side measuring $8m.$

Answer

A regular hexagon is a closed polygon having six sides of equal lengths.
Side of the hexagon $= 8m$
Perimeter of the hexagon $= 6($Side of the hexagon$) = 6 \times 8 = 48m$

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Question 212 Marks

Find the perimeter of the square whose side is given below: $10\ cm$

Answer

Perimeter of a square $= 4 \times ($Length of one side$)$
Length of one side $= 10\ cm$
Perimeter $= 4 \times 10 = 40\ cm$

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Question 222 Marks

Find the area of a rectangle,
whose Length $= 8\ cm,$
breadth $= 3\ cm$

Answer

Area of a rectangle $= ($Length $\times $ Breadth$)$
Length $= 8\ cm$
Breadth $= 3\ cm$
Area of rectangle $= 8 \times 3$
$ = 24\ cm^2$

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Question 232 Marks

Find the breadth of the rectangle whose perimeter is $360\ cm$ and whose length is: $102\ cm$

Answer

Perimeter of a rectangle $= 2($Length $+$ Breadth$)$
Therefore, Breadth of the rectangle $=\frac{\text{Perimeter}}{2}-\text{Length}$
Perimeter $= 360\ cm$
Length $=\frac{10}{2}$
Breadth $=\frac{360}{2}-140$
$= 180 - 102 = 78\ cm$

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Question 242 Marks

Split the following shape into rectangles and find the area. (The measures are given in centimeter.)

Answer

This figure consists of two squares $I$ and $III$ and one rectangle $II.$

Area of square $I =$ Area of square $III = ($Side $\times $ Side$)$
$= 7 \times 7$
$ = 49\ cm^2$
Similarly, area of rectangle $II = ($Length $\times $ Breadth$)$
$= (21 \times 7)$
$= 147\ cm^2$ Thus, total areas of this figure $= ($Area of square $I\ +$ Area of rectangle $II\ +$ Area of square $III)$
$= 49 + 49 + 147$
$ = 245\ cm^2$

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Question 252 Marks

Find the area of a rectangle, whose Length $= 6\ cm,$ breadth $= 3\ cm$

Answer

Area of a rectangle $= ($Length $\times $ Breadth$)$
Length = $6\ cm,$
Breadth $= 3\ cm$
Area of rectangle $= 6 \times 3$
$= 18\ cm^2$

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Question 262 Marks

The following figure is drawn on a squared paper. Count the number of square enclosed by figure and find its area, taking the area of square as $1\ cm^2$.

Answer

There are $13$ complete squares, $8$ more than half squares and $7$ less than half squares in the given shape.
Area of one square $= 1\ cm^2$
Area of this shape $= (13 + 8 \times 1) = 21\ cm^2$

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Question 272 Marks

Find the perimeter of the square whose side is given below: $115.5\ cm$

Answer

Perimeter of a square $= 4 \times ($Length of one side$)$
Length of one side $= 115.5\ cm$
Perimeter $= 4 \times 115.5 = 462\ cm$

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Question 282 Marks

The area of a rectangle is $49\ cm^2$ and its breadth is $2.8\ cm.$ Find the length of the rectangle.

Answer

Area $= 49\ cm^2$
Breadth $= 2.8\ cm$
Area of the rectangle $= ($Length $\times $ Breadth$)$
$\therefore\text{Length}=\frac{\text{Area}}{\text{Breadth}}$
$=\frac{49}{2.8}=17.5\text{cm}$

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Question 292 Marks

Find the perimeter of the following figure:

Answer

Perimeter of the figure $= (AB + BC + CD + DE + EF + FG + GH + HA) = 10 + 10 + 20 + 30 + 20 + 20 + 10 + 20 = 140m$

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Question 302 Marks

Split the following shape into rectangles and find the area. (The measures are given in centimeter)

Answer

This figure consists of two rectangles $I$ and $II.$

Area of rectangle $I = ($Length $\times $ Breadth$)$
$= 5 \times 1$
$= 5\ cm^2$
Similarly, area of rectangle $II = ($Length $\times $ Breadth$)$
$= 4 \times 1$
$= 4\ cm^2$
Thus, total area of this figure $= ($Area of rectangle $I +$ Area of rectangle $II)$
$= 5 + 4$
$= 9\ cm^2$

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Question 312 Marks

Find the perimeter of the rectangle whose lengths and breadths are given below: $7\ cm, 5\ cm$

Answer

Perimeter of a rectangle $= 2 \times ($Length $+$ Breadth$)$
Since, Length $= 7\ cm,$
Breadth $= 5\ cm$
Therefore, Perimeter $= 2(7 + 5) = 2(12) = 24\ cm$

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Question 322 Marks

The following figure is drawn on a squared paper. Count the number of square enclosed by figure and find its area, taking the area of square as $1\ cm^2$.

Answer

There are $8$ complete squares, $6$ more than half squares and $4$ less than half squares in the given shape.
Area of one square $= 1\ cm^2$
Area of this shape $= (8 + 6 \times 1) = 14\ cm^2$

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Question 332 Marks

Find the breadth of the rectangle whose perimeter is $360\ cm$ and whose length is: $140\ cm$

Answer

Perimeter of a rectangle $= 2($Length $+$ Breadth$)$
Therefore, Breadth of the rectangle $=\frac{\text{Perimeter}}{2}-\text{Length}$
Perimeter $= 360\ cm$
Length $= 140\ cm$
Breadth $=\frac{360}{2}-140$
$= 180 - 140 = 40\ cm$

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