Chapter 6: Mensuration

Ans: Area of rectangle $= L \times B$

$=5cm\times 3cm=15{cm}^{2}$

Ans:  Area of rectangle$ = L\times B$

$=6 \times 2 = 12{unit}^{2}$

Ans: Given,a rectangle and a square have the same perimeter.

So, $2\times(L + B)=4 \times $ sides

Side =$\dfrac{2(L+B)}{4}$

Side =$\dfrac{2(6+2)}{4}$

Side =$\dfrac{2 \times 8}{4}$

Side =$\dfrac{16}{4}$

Side =4unit

Area of Square = $(sides)^{2}$

=$(4unit)^{2}$ = 16$unit^{2}$

Ans: 1m = 100 cm.

Ans: 1sqcm=1cm$\times$ 1cm.

Ans: 1 sqm =1m $\times$ 1m = 100 cm $\times$ 100 cm.

Ans: 1 sqm= 10000 sq cm.

In questions 14 to 20, state which of the statements are true and which are false.

Ans: True

Let. $L$ and $B$ are the length and breadth of the old rectangle and $L ^{\prime}$ and B' length and breadth of the new rectangle.

Than,according to the question

$L ^{\prime}=\dfrac{1}{2} L$ and $B ^{\prime}=2 B$

So,the area of given rectangle=$L \times B$

And area of new rectangle $= L^{\prime} \times B ^{\prime}=\dfrac{1}{2} L \times 2 B = L \times B$

Hence, the area of the rectangle obtained remains the same.

Ans: False

Let, the side of square is $A$

Than area of square $= A ^{2}$

According to the question,if the side of the square is doubled

The side of new square is $=2 A$

And area of new square $=(2 A )^{2}=4 A ^{2}$

Ans: False

Sides = 8

So, perimeter Of hexagon $=8\times sides$

$8 \times 6=48 cm$

Ans: True

Because ,perimeter is the measure of the boundary.

Ans: False

He must find the perimeters of the compound, not the area.

Ans: False

Because,to find the cost of painting a wall we need to find the Area of the wall,not perimeter.

Ans: True

Because to find the cost of a frame of a picture, we need to find the perimeter of the picture.