Chapter 6: Mensuration

Ans:Given that each square is of unit length,$ABCD$ is 10 units and breadth is 6 units

Perimeter of $ABCD = 2 \times($ length $+$ breadth $)$

$=2 \times(10+6)$ units $=2 \times 16$ units $=32$ units

Ans:Area of rectangle $ABCD =$ length $\times$ breadth

$(10 \times 6) \text { units }^{2}=60 \text { units }^{2}$

(c) Divide this rectangle into ten parts of the equal area by shading squares.

(Two parts of equal area are shown here)

Ans: The figure shows the part of the rectangle of the equal area by shading squares 1,2, 3, 4, 5, 6, 7, 8, 9 and 10.

Ans: For 1,2,4,7,8 & 10 parts, Perimeter is 12 units.

For 3,5,6 & 9 Perimeter is 14 units.

No, they are not equal.

Ans: Area of square tile=$15\times 15$=225$cm^{2}$

Number of tile $=28$ square 

So, area of the wall $=(225 \times 28) cm ^{2}$ $=6300 cm ^{2}$

Ans: Given,Length ($L$)=120cm and breadth=$B$

Than,L=$6 B$ 

$B =\dfrac{120}{6} =20 cm$ 

Perimeter of the rectangle $=2 \times( L + B )$ 

$2 \times(120+20) =2 \times 140  =280 cm$

Ans: The area of the Anmol's chart paper =$(90 cm \times 40 cm )=3600 cm ^{2}$ 

The area of the Abhishek's chart paper= $(50 cm \times 70 cm )=3500 cm ^{2}$ 

So,Anmol will cover more area on the table and by how 100 cm $^{2}$. 

Ans: Given length ($L) =60 m =6000 cm$

Width($B)=3 m =300 cm$

Side of the square tile $=25 cm$

Number of tiles in one row along width

$\dfrac{\text { width of the path }}{\text { side of the a tile }}=\dfrac{300}{25}=12$

$\text {Number of the rows}=\dfrac{\text {length of the path}}{\text{side of a tile }}=\dfrac{6000}{25}=240$

Number of tiles=$12\times 240=2880$

Ans: Given,side of square slab=90cm

Area of square slab $=(90 cm )^{2}=8100 cm ^{2}$

And,area of the floor$=81 m ^{2}=81 \times 10000 cm ^{2}$

$=810000 cm ^{2}$

Number of slab=$\dfrac{\text { Area of the floor }}{\text { Area of square slab }}$

$=\dfrac{810000}{8100}=100 \text { slabs }$

Ans: Given,length(L)=8m

Width(B)=2m

Than,perimeter=$2(L+B)$=$2(8+2)=2\times 10=20m$

And,area=$L \times B$=$8 \times 2$=$16m^{2}$

According to the question

Perimeter=Perimeter of a rectangular

$4\times Side$=20

$Side=\dfrac{20}{4}$=$5m$

Now,area of square=$Side\times Side$=$5\times 5=25m^{2}$

Hence,the area of a square field is greater than the area of a rectangular field.

Ans: Given , perimeter of the square $=800 m =4 \times$ sides

$800 m =4 \times \text { sides }$

$\text { side }=\dfrac{800}{4} =200 m$

And area of square $=Side\times Side=(200 m )^{2}=40000 m ^{2}$

Ans: Given,side of square  $=5 cm$

Than,area of square $=Side\times Side=5\times 5=25 cm ^{2}$....(i)

According to the question

New side=$2\times old  side$

$=2\times 5=10cm$

Now,area of square $=10\times 10=100 cm ^{2}$

By,(i) and (ii) area of the new square is increased by 4 times.

Ans: Given,area of square chart=$60\times 60=3600cm^{2}$

Length of the chart is $60 cm$ and in that 7 cards of 8 cm length she can make and for width $60 cm$ she can make exactly 12 cards of length 5cm.

So total no. of cards $= 12 \times 7 =84$

And area of card=$8\times 5=40cm^{2}$

The area of left part of square chart$=3600 -(84\times 40)=240cm^{2}$