Area And Its Boundary - Class 5 Maths - Extra Questions

Divide these rectangles into two triangles with equal area.
695905_d48d5068669342aabce2ec99d0cef78c.png

The rectangles are divided into 2 triangles of equal areas.
725359_695905_ans_829591d622aa4da28e77af9e4a518ef1.png


Which stamp covers the smallest area?
695898_f12fcf87dc21413e927ae990fc96bb06.png

Stamp A covers $$6$$ squares of $$1$$cm side , Stamp C cover $$1$$ square , Stamp B covers $$2$$ squares and Stamp D covers $$4$$ squares.
So ,smallest area is covered by stamp C


Find the total number of squares covered by all the stamps and hence find the total area covered.
695897_e7552259c57140a9b25e8ae738ea70d0.png

Stamp A covers $$6$$ squares of $$1$$ cm side , Stamp C cover $$1$$ square , Stamp B covers $$2$$ squares and Stamp D covers $$4$$ squares.
So ,total squares covered are $$\left( 6+1+2+4 \right) =13$$
So total area = $$\left( 1\times 13 \right) =13\ square\ cm$$


How many squares of $$1$$cm side does stamp B cover?
695895_9a1ecdc5304149b78d6a86ea00269746.png

It is clear from the figure that the stamp B covers $$2$$ squares of $$1$$ cm side each.
Hence the answer is $$2$$



How many squares of $$1$$cm side does stamp A cover?
695894_eeaf683ea90d478da66bfe6b7995601f.png

It is clear from the figure that the Stamp A covers $$6$$ squares of $$1$$ cm side each.
Hence the answer is $$6$$


What is the area of each of the smaller rectangles?
695904_d87609aa8e0542c7911fc483c0ddf384.png

Consider the side of square box to be  1 cm then area of each square box is 1 square cm
Each smaller  rectangle contains 12 boxes so the area of smaller rectangle will be $$\left( 12\times 1 \right) =12\quad sq\quad cm$$

725357_695904_ans_d371242ef0e8464da644cc0713782138.png


Find the area of the rectangle whose length = 42.4 cm , breadth = 15.6 cm .

Area of rectangle = $$length \times breadth$$
                              = $$42.4 \times 15.6$$ = $$661.44$$ $$cm^{2}$$


Divide these rectangles into two smaller rectangles of equal area.
695903_2522c5c02a8a4abd82e283f6485247fc.png

The rectangles are  divided into two smaller rectangles each rectangle containing 6 square boxes .
725353_695903_ans_eb54e9aefd3847a28de5f6689f4ff75c.png


Which stamp covers the largest area? ___________.
695896_db6450907e3a46eda203f4cc5284a642.png

Stamp A covers 6 squares of 1 cm side , Stamp C cover 1 square , Stamp B covers 2 squares and Stamp D covers 4 squares.
So ,largest area is covered by stamp A


What is the difference in the area of biggest and smallest stamp?
695900_f316c1bc60d24a6ab075007cd442407e.png

Stamp A covers $$6$$ squares, Stamp C cover $$1 $$square , Stamp B covers $$2$$ squares and Stamp D covers$$ 4$$ squares.
So, the area of biggest stamp,stamp A =$$\left( 6\times 1\right) =6\quad square\quad cm$$
And ,the area of smallest stamp ,stamp C = $$\left( 1\times 1\right) =1\quad square\quad cm$$
Difference in the area of the biggest and smallest stamp
$$=(6-1)= 5\ square\ cm$$


$$ 1\, m^2$$ ______ $$cm^2$$.

We know that $$1 m =.100\,cm$$
$$1m^2  =(100)^2 \, cm^2$$
$$\Rightarrow  1m^2 = (100)^2 \, cm^2$$
$$ \Rightarrow 1m^2 = 10000\, cm^2$$


$$1\ cm^2 =$$ ______ $$mm^2 $$

$$\Rightarrow  1 cm =10 \, mm$$
$$ \Rightarrow 1cm^2 = (10)^2\, mm^2$$
 $$\Rightarrow 1 \, cm^2 = 100 \, mm^2$$


The side of the small squares is $$1$$ cm. Find the total area covered by the shaded region.
695908_38ab1818c7d44cc2a288e48268e9ad71.png

There are $$2$$ rectangles, each of these rectangles contains $$8$$ square boxes in total 
The side of each square box is $$1$$ cm
thus area of each square $$=1$$ sq cm
Then the area of each rectangle will be $$(8\times1)\ sq.cm=8\ sq.cm$$

Thus the area of $$2$$ rectangles $$=( 2\times8)\ sq.cm=16\ sq.cm$$

Hence, the area of the shaded region is $$ 16\ sq.cm$$


Two fields have the same perimeter. One is a square of side $$72$$m and another is a rectangle of length $$80$$m. Which plot has the greater area and by how much?


1305171_701450_ans_acf64e184a0440dc9ccd1e86ef94f3af.jpg


Which stamp has biggest area?____________________ ?

1109651_f8e729b8d1f741dabf4ad77c5c870c11.png

$$A$$ is the answer which has a biggest area.


What is the area of the triangle?
695906_2b63823d921548a8a49802e9d7ca602a.png

area of the triangles in the first figure will be  $$2\div 2=1sq\quad cm$$
since the figure consists of two square boxes each having area of 1 sq cm
Area of triangles in second figure will be  $$6\div 2=3sq\quad cm$$
since the figure contains 6 square boxes
Area of triangles in third figure will be  $$12\div 2=6 sq\quad cm$$
since the figure contains 12 square boxes

725366_695906_ans_dcdc3b68674240d18155a81b6ae5dded.png


A wire is in shape of a rectangle. Its length is $$40\,cm$$ and breadth is $$22\,cm$$. If the same wire is reshaped into a square, what will be the measure of each side. Also find which shape encloses more area.

Given, 
Length of rectangle$$(l)=40\ cm$$
Breadth of rectangle$$(b)=22\ cm$$

Perimeter of rectangle$$=2(l+b)$$
                                      $$=2(40+22)\ cm$$
                                      $$=124\ cm$$
It is reshaped into square

$$\therefore$$ Perimeter remains same
Let, the edge of square be $$a$$
$$\therefore 4a=124$$
$$\Rightarrow a=31$$

Hence, the side of square is $$31\ cm$$ .

Area of rectangle$$=l\times b$$
                             $$=40\times 22\ sq.cm$$
                             $$=880\ sq.cm$$

Area of square$$=Side\times Side$$
                         $$=31\times 31\ sq.cm$$
                         $$=961\ sq.cm$$

Hence, the square encloses more area.


Find the area of the region enclosed by the following figure by counting squares. 
1801409_1888d175d7fa4c4bb1e64119c65816ce.PNG

(i) CoverNumber estimateArea
(a) Full-filled squares99 sq. units
(b) Half-filled squares______
(c) More than half-filled squares______
(d) Less than half-filled squares______
$$\therefore$$ Total area of the figure = 9 sq. units.



(ii) CoverNumber estimateArea
(a) Full-filled squares55 sq. units
(b) Half-filled squares______
(c) More than half-filled squares______
(d) Less than half-filled squares______
$$\therefore$$ Total area of the figure = 5 sq. units.


(iii) Fill-filled squares = 10 
$$\therefore$$ Total area = Area covered by full squares
= 10 $$\times$$ 1 sq. unit =10 sq. units 


(iv) Full-filled squares = 4
Half-filled squares = 4
Area covered by full squares = 4 $$\times$$ 1 sq. unit = 4 sq.
units Area covered by half squares = 4 $$\times \frac{1}{2}$$ sq. units = 2 sq. units
$$\therefore$$ Total area = 4 sq. units + 2 sq. units = 6 sq. units 


(v) Full-fulled squares = 2
Half-filled squares = 4
Area covered by full squares = 2 $$\times$$ 1 sq. unit = 2 sq. units
Area covered by half squares = 4 $$\times \frac{1}{2}$$ sq. unit = 2 sq. units
$$\therefore$$ Total area = 2 sq. units + 2 sq. units = 4 sq. units. 


(vi) Full-filled squares = 3
Half-filled squares = 6
Area covered by full squares = 3 $$\times$$ 1 sq. unit = 3 sq. units
Area covered by half squares = 6 $$\times \frac{1}{2}$$ sq. unit = 3 sq. units
$$\therefore$$ Total area = 3 sq. units + 3 sq. units = 6 sq. units 


$$10\, cm^2 =$$ ________ $$m^2$$.

We know that $$ 1\, cm =\cfrac {1}{100}\, m$$
$$\Rightarrow  10\, cm^2 = 10 \times \left ( \cfrac {1}{100} \right )^2 m^2$$
$$ \Rightarrow 10\, cm^2 = 10\times \cfrac1{10000}\, m^2 $$
$$\Rightarrow 10\, cm^2 = 0.001 \, m^2$$


Find the areas of the following figures by counting the square.

1868821_60bfe170ff464c9e9aefb4c1423ba1a8.png

The figure contains $$5$$ fully filled squares only. Therefore, the area of this figure will be $$5$$ square units.


The region given in figure is measured by taking each rectangular box as a unit. What is the area of the region?
1790028_3b993a29013144d78248f77ef851c792.png

Area of 1 small rectangle = 1 square unit

Total number of small rectangles = 13

$$\therefore$$ Area of region =  Total number of small rectangles $$\times$$ Area of 1 small rectangle
                        $$= (13 \times 1)$$
                        $$= 13$$ square units
 
$$\therefore \textbf{Area of the region is 13 square units}$$


Find the areas of the following figures by counting the square.
1868823_f133b782b837431db1af1a8e58b03268.png

The figure contains $$2$$ fully filled squares and $$4$$ half-filled squares.
total squares = 2 full squares + 4 x half squares = 2 full squares + 2 full squares = 4 full squares
Therefore, the area of this figure will be $$4$$ square units.


Rectangular wall MNOP of a kitchen is covered with square tiles of 15 cm length (Figure above). Find the area of the wall.
1790367_43e95675fef64698aad1dbdf74b7468e.png

SOLVED] Rectangular wall MNOP of a kitchen is covered with square tiles of 15 cm length (Figure above). Find the area of the wall.

It can be observed that MN and MP are the length and breadth of rectangle MNOP.
Number of squares along MN = 7
Number of squares along MN = 4

$$\therefore$$ Length of rectangle MNOP (MN) = Number of squares along MN $$\times$$ length of each square
                                              $$= (7 \times 15)cm$$
                                              $$= 105\ cm$$
                                              
                Breadth of rectangle MNOP (MP) = Number of squares along MP $$\times$$ length of each square
                                                $$= (4 \times 15)cm$$
                                                
                                                $$= 60\ cm$$
                                                
                   Area of rectangle MNOP = Length $$\times$$ Breadth
                                           $$= MN \times MP$$
                                               $$=(105 \times 60)cm^2$$
                                                 
                                               $$=6300\ cm^2$$
$$\therefore \textbf{Area of wall is }6300 cm^2$$


Find the areas of the following figures by counting square.
1868830_ec3bfa604101427fa7136ad9217a129a.png

The figure contains $$9$$ fully filled squares only. Therefore, the area of this figure will be $$9$$ square units.


Find the areas of the following figures by counting square.
1868827_0323419dcf584affa0659f1075adb30a.png

The figure contains $$2$$ fully filled squares and 4 half-filled squares. Therefore, the area of this figure will be $$4$$ square units.


Find the perimeter of the above figure if each square has an edge of 1 cm.

1868829_3631c639de194bcf9c94bfd4cd55234c.png

As from the figure we can see, the perimeter of the figure is $$(1 \ cm \  \times 12)=12 cm$$
1957571_1868829_ans_da0c27175167486a837ec713198dda49.PNG


Find the areas of the following figures by counting square.
1868824_46c8828d9f2b47b9abde5515dc403670.png

The figure contains $$8$$ fully filled squares only. Therefore, the area of this figure will be $$8$$ square units.


Find the areas of the following figures by counting square.
1868825_99d3bc589a8a46d6a2d4469050d71816.png

The figure contains $$10$$ fully filled squares only. Therefore, the area of this figure will be $$10$$ square units.


Find the areas of the following figures by counting square.
1868831_9bb3934f42524b0584e25313e0359b09.png

The figure contains $$2$$ fully filled squares and $$4$$ half-filled squares. Therefore, the area of this figure will be $$4$$ square units.


Find the areas of the following figures by counting square.
1868833_a665ed8551244af887820e3be7fa403a.png

The figure contains $$4$$ fully filled squares and $$2$$ half-filled squares. Therefore, the area of this figure will be $$5$$ square units.


Split the following shapes into rectangles and squares. Find their area .(All measurements are given in centimeters).
1566454_c351bc8d616043dcb8a654c831f61f07.png


2044585_1566454_ans_6d357aa9b62e4103a9baa51968df2056.jpg


Class 5 Maths Extra Questions