*Q1. What is the area of the following rectangles whose sides’ measure: *

(a) 2 cm and 5 cm

(b) 15 m and 20 m

(c) 4 km and 5 km

(d) 3 m and 60 cm

** Ans: ** It is known that, Area of a rectangle = Length (

*l*) x Breadth (

*b*)

*(a) l* = 2 cm

*b* = 5 cm

Area = *l* x *b* = 2 x 5 = 12 cm^{2}

(b) *l* = 15 m

*b*= 20 m

Area = *l* x *b*= 20 x 15 = 300 m^{2}

(c) *l* = 4 km

*b*= 5 km

Area = l x b = 4 x 5 = 20 km^{2}

(d) *l* = 3 m

*b* = 60 cm = 0.60 m

Area = l x b=2 x 0.60 = 1.20 m^{2}

*Q2. Find the areas of the squares whose sides are: (a) 8 cm (b) 11 cm (c) 6 m *

*Ans:*

It is known that, Area of a square = (Side)^{2}

(a) Side = 8 cm Area = (8)^{2} =64 cm^{2}

(b) Side = 11 cm Area = (11)^{2 }= 121 cm^{2}

(c) Side = 6 m Area = (6)^{2} = 36 m^{2}

*Q3. Which one has the largest and smallest area among the 3 rectangles whose dimensions measure:*

(a) 5 m by 6 m

(b) 12m by 4 m

(c) 2 m by 10 m

** Ans:** We know that, Area of rectangle = Length x Breadth

(a) l = 5m

b = 6m

Area = l x b = 5 x 6 = 30 m^{2}

(b) l = 12m

b = 4m

Area = l x b = 12 x 4 = 48 m^{2}

(c) l = 2m

b = 10m

Area = l x b = 2 x 10 = 20 m^{2}

From the above results, we come to know that (b) has the largest area and rectangle (c) has the smallest area.

*Q5: What is the cost of tiling a rectangular plot of land 400 m long and 300 m wide at the rate of Rs 5 per hundred sq in? *

** Ans**:

Area of rectangular plot = 400 x 300 = 120000 m^{2}

Cost of tiling per 100 m^{2} = Rs 5

Cost of tiling per 120000 m^{2} = \(\frac{5}{100}\times 120000 = Rs.6000\)

*Q6: What is the area of table whose sides measure 1m 20 cm in length and 2m 50 cm in breadth? *

*Ans: *

Length (l) = 1 m 20cm = \((1+\frac{20}{100})\ m = 1.2\ m\)

Breadth (b) 2 m 50 cm = \((2+\frac{50}{100})\ m = 2.5\ m\)

Area = l x b = 1.2 x 2.5 = 3 m^{2}

* *

*Q7: How many sq meters of carpet is needed to cover the floor of a room of sides measuring 3 m in length and 4 m 20cm in breadth? *

*Ans:*

Length (l) = 3 m

Breadth (b) = 4 m 20 cm = \((4+\frac{20}{100})\ m = 4.2\ m\)

Area = l x b = 3 x 4.2 = 12.6 m^{2}

*Q8: A square carpet is laid on the floor of sides measuring 4 m in a floor of sides 4 m and 5 m. Find the remaining area of the floor that is not carpeted. *

*Ans:*

Length (I) = 4 m

Breadth (b) = 5 m

Area of floor = l x b = 4 x 5 = 20 m^{2}

Area covered by the carpet = (Side)^{ 2} = (4)^{2} = 16 m^{2}

Area not covered by the carpet = 20 – 16 = 4 m^{2}

*Q9: From a piece of land measuring 4 m long and 6 m wide, 4 sq flower beds of side 2m each are dug out. Find out the remaining area of the land. *

*Ans:*

Area of the land = 4 x 6 = 24 m^{2}

Area occupied by 4 flower beds = 4 x (Side)^{2} = 4x (2)^{2} = 16m^{2}

Area of the remaining part = 24 – 16 = 8 m^{2}

*Q10: Split the below figures into multiple rectangles and find out their area. All dimensions are given in centimeters.*

*Ans: *

(a) The above figures can be split in to multiple rectangles as follows:

Area of 1^{st} rectangle = 8 x 4 = 32 cm^{2}

^{ }Area of 2^{nd} rectangle = 12 x 2 = 24 cm^{2}

Area of 3^{rd} rectangle = 6 x 4 = 24 cm^{2}

Area of 4^{th} rectangle = 8 x 4 = 32 cm^{2}

Total area of the whole figure = 32 + 24 + 24 + 32 = 112 cm^{2}

(b) The above figures can be split in to multiple rectangles as follows:

Area of 1^{st} rectangle = 6 x 2 = 12 cm^{2}

^{ }Area of 2^{nd} rectangle = 6 x 2 = 12 cm^{2}

Area of 3^{rd} rectangle = 6 x 2 = 12 cm^{2}

Total area of the whole figure = 12 + 12 + 12 = 36 cm^{2}

*Q11. Split the below figures into multiple rectangles and find out their area. All dimensions are given in centimeters.*

*Ans: *

(a) The above figures can be split in to multiple rectangles as follows:

Area of 1^{st} rectangle = 24 x 4 = 96 cm^{2}

^{ }Area of 2^{nd} rectangle = 16 x 4 = 64 cm^{2}

Total area of the whole figure = 96 + 64 = 160 cm^{2}

(b) The above figures can be split in to multiple rectangles as follows:

Area of 1^{st} rectangle = 42 x 14 = 588 cm^{2}

^{ }Area of 2^{nd} rectangle = 14 x 14 = 196 cm^{2}

Area of 3^{rd} rectangle = 14 x 14 = 196 cm^{2}

Total area of the whole figure = 588 + 196 + 196 = 980 cm^{2}

(c) The above figures can be split in to multiple rectangles as follows:

Area of 1^{st} rectangle = 10 x 2 = 20 cm^{2}

^{ }Area of 2^{nd} rectangle = 8 x 2 = 16 cm^{2}

Total area of the whole figure = 20 + 16 = 36 cm^{2}

**Q12. Tiles of sides measuring 10 cm by 4 cm each are to be fit in a rectangular region whose length and breadth are respectively:**

**(a) 144 cm and 100 cm**

**(b) 36 cm and 70 cm**

Ans. (a) Total area of the region = 144 x 100 = 14400 cm2

Area of one tile = 10 x 4 = 40 cm^{2}

Number of tiles required = \(\frac{14400}{40}\) = 360

Therefore, 360 tiles are required.

(b) Total area of the region = 36 x 70 = 2520 cm^{2 }

Area of one tile = 40 cm^{2}

Number of tiles required = \(\frac{2520}{40}\) = 63

Therefore, 63 tiles are required.