Question

Find in hectares the area of a rectangle of length 9 dam and breadth 21 CM

Answer 1

Find the area, in square meters, of a rectangle whose

(i) Length = 5.5 m, breadth = 2.4 m

(ii) Length = 180 cm, breadth = 150 cm

 

A1: We have,

(i) Length = 5.5 m, Breadth = 2.4 m Therefore, Area of rectangle = Length x Breadth = 5.5 m x 2.4 m = 13.2 m2

(ii) Length = 180 cm = 1.8 m, Breadth = 150 cm = 1.5 m [ Since 100 cm = 1 m] Therefore, Area of rectangle = Length x Breadth = 1.8 m x 1.5 m = 2.7 m2

Q2: Find the area, in square centimeters, of a square whose side is        

(i) 2.6 cm

(ii) 1.2 dm

 

A2: We have,

(i) Side of the square = 2.6 cm

Therefore, area of the square = (Side)2 = (2.6 cm)2= 6.76 cm2

(ii) Side of the square = 1.2 dm = 1.2 x 10 cm = 12 cm

Therefore, area of the square = (Side)2 = (12 cm)2= 144 cm2         [ Since 1 dm = 10 cm]

 

Q3:  Find in square metres, the area of a square of side 16.5 dam.

 

A3: We have,

Side of the square = 16.5

dam = 16.5 x 10 m = 165 m

Area of the square = (Side)2 = (165 m)2 = 27225 m2

[Since 1 dam/dm (decameter) = 10 m ]

Q4: Find the area of a rectangular field in acres whose sides are:

(1) 200 m and 125 m

(ii) 75 m 5 dm and 120 m

 

A4 : We have,

(i) Length of the rectangular field = 200 m

Breadth of the rectangular field = 125 m

Therefore, Area of the rectangular field = Length x Breadth = 200 m x 125 m

= 25000 m2 = 250 acres [Since 100 m2 = 1 are]

(ii) Length of the rectangular field =75 m 5 dm = (75 + 0.5) m

= 75.5 m [Since 1 dm = 10 cm = OA m]

Breadth of the rectangular field = 120 m

Therefore, Area of the rectangular field = Length x Breadth

= 75.5 m x 120 m = 9060 m2 = 90.6 acres  [Since 100 m2 = 1 are]

Q 5:  Find the area of a rectangular field in hectares whose sides are:

(i) 125 m and 400 m

(ii) 75 m 5 dm and 120 m

 

A 5 : We have,

(i) Length of the rectangular field = 125 m

Breadth of the rectangular field = 400 m

Therefore, Area of the rectangular field = Length x Breadth

= 125 m x 400 m = 50000 m2 = 5 hectares [Since 10000 m2 = 1 hectare]

(ii) Length of the rectangular field =75 m 5 dm = (75 + 0.5) m

= 75.5 m [Since 1 dm = 10 cm = 0.1 m]

Breadth of the rectangular field = 120 m

Therefore, Area of the rectangular field = Length x Breadth

= 75.5 m x 120 m = 9060 m2 = 0.906 hectares [Since 10000 m2 = 1 hectare]

Q6: A door of dimensions 3 m x 2m is on the wall of dimension 10 m x 10 m. Find the cost of painting the wall if rate of painting is Rs 2.50 per sq. m.

 

A 6 :  We have,

Length of the door = 3 m

Breadth of the door = 2 m

Side of the wall = 10 m

Area of the wall = Side x Side = 10 m x 10 m

= 100 m2

Area of the door = Length x Breadth = 3 m x 2 m = 6 m

Thus, required area of the wall for painting = Area of the wall – Area of the door

= (100 – 6) m2= 94 m2

Rate of painting per square metre = Rs. 2.50

Hence, the cost of painting the wall = Rs. (94 x 2.50) = Rs. 235

Q7: A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is bent in the shape of a square, what will be the measure of each side? Also, find which side encloses more area?

 

A7 : We have,

Perimeter of the rectangle = 2(Length + Breadth)

= 2(40 cm + 22 cm) = 124 cm

It is given that the wire which was in the shape of a rectangle is now bent into a square.

Therefore, the perimeter of the square = Perimeter of the rectangle

=> Perimeter of the square = 124 cm

4 x side = 124 cm

Side = 124/4 = 31 cm

Now, Area of the rectangle = 40 cm x 22 cm = 880 cm2

Area of the square = (Side)2 = (31 cm)2 = 961 cm2.

Therefore, the square-shaped wire encloses more area.

Q8: How many square metres of glass will be required for a window, which has 12 panes, each pane measuring 25 cm by 16 cm?

 

A8: We have,

Length of the glass pane = 25 cm

Breadth of the glass pane = 16 cm

Area of one glass pane = 25 cm x 16 cm

= 400 cm2 = 0.04 m2

[Since 1 m2 = 10000 cm2 ]

Thus, Area of 12 such panes = 12 x 0.04 = 0.48 m2

Answer 2



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Find in hectares the area of a rectangle of length 9 dam and breadth 21 CM

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 by Rajdogra72 3 minutes ago

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Expert

Find the area, in square meters, of a rectangle whose

(i) Length = 5.5 m, breadth = 2.4 m

(ii) Length = 180 cm, breadth = 150 cm

 

A1: We have,

(i) Length = 5.5 m, Breadth = 2.4 m Therefore, Area of rectangle = Length x Breadth = 5.5 m x 2.4 m = 13.2 m2

(ii) Length = 180 cm = 1.8 m, Breadth = 150 cm = 1.5 m [ Since 100 cm = 1 m] Therefore, Area of rectangle = Length x Breadth = 1.8 m x 1.5 m = 2.7 m2

Q2: Find the area, in square centimeters, of a square whose side is        

(i) 2.6 cm

(ii) 1.2 dm

 

A2: We have,

(i) Side of the square = 2.6 cm

Therefore, area of the square = (Side)2 = (2.6 cm)2= 6.76 cm2

(ii) Side of the square = 1.2 dm = 1.2 x 10 cm = 12 cm

Therefore, area of the square = (Side)2 = (12 cm)2= 144 cm2         [ Since 1 dm = 10 cm]