The document RD Sharma Solutions (Part - 1) - Ex-20.1, Mensuration - I, Class 7, Math Class 7 Notes | EduRev is a part of the Class 7 Course RD Sharma Solutions for Class 7 Mathematics.

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**Find the area, in square metres, of a rectangle whose(i) Length = 5.5 m, breadth = 2.4 m(ii) Length = 180 cm, breadth = 150 cm**

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 m^{2}^{ }

(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 m^{2}

**Find the area, in square centimetres, of a square whose side is(i) 2.6 cm(ii) 1.2 dm**

We have,

(i) Side of the square = 2.6 cm

Therefore, area of the square = (Side)^{2}

= (2.6 cm)^{2 }= 6.76 cm^{2}

(ii) Side of the square = 1.2 dm = 1.2 x 10 cm = 12 cm [ Since 1 dm = 10 cm]

Therefore, area of the square = (Side)^{2}

= (12 cm)^{2 }= 144 cm^{2}

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

We have,

Side of the square = 16.5 dam = 16.5 x 10 m = 165 m [ Since 1 dam = 10 m ]

Area of the square = (Side)^{2} = (165 m)^{2}

= 27225 m^{2}

**Find the area of a rectangular feild in ares whose sides are:(i) 200 m and 125 m(ii) 75 m 5 dm and 125 m**

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 m^{2} = 250 ares [Since 100 m^{2} = 1 are]

(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 m^{2} = 90.6 ares [Since 100 m^{2} = 1 are]

**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**

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 m^{2} = 5 hectares [Since 10000 m^{2} = 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 m^{2} = 0.906 hectares [Since 10000 m^{2} = 1 hectare]

**A door of dimensions 3 m Ã— 2m is on the wall of dimension 10 m Ã— 10 m. Find the cost of painting the wall if rate of painting is Rs 2.50 per sq. m.**

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 m^{2}

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

Thus,

Required area of the wall for painting = Area of the wall âˆ’ Area of the door = (100 âˆ’ 6 ) m^{2}^{ }= 94 m^{2}

Rate of painting per square metre = Rs. 2.50

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

**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?**

We have,

Perimeter the of 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

â‡’ 4 x side = 124 cm

âˆ´ Side = 124/4=31 cm

Now,

Area of the rectangle = 40 cm x 22 cm = 880 cm^{2}

Area of the square = (Side)^{2} = (31 cm)^{2} = 961 cm^{2}

Therefore, the square-shaped wire encloses more area.

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

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 cm^{2} = 0.04 m^{2}^{ } [ Since 1 m^{2} = 10000 cm^{2} ]

Thus,

Area of 12 such panes = 12 x 0.04 = 0.48 m^{2}

**A marble tile measures 10 cm Ã— 12 cm. How many tiles will be required to cover a wall of size 3 m Ã— 4 m? Also, find the total cost of the tiles at the rate of Rs 2 per tile.**

We have,

Area of the wall = 3 m x 4 m = 12 m^{2}

Area of one marble tile = 10 cm x 12 cm = 120 cm^{2} = 0.012 m^{2} [ Since 1 m^{2} = 10000 cm^{2} ]

Thus,

Number of tiles =

Cost of one tile = Rs. 2

Total cost = Number of tiles x Cost of one tile

= Rs. (1000 x 2) = Rs. 2000