Area Made Simple : With Word Problems For Class 6th,7th,8th,9th [1]

FORMULAS:

1) Area of rectangle = L*B
2) Area of square = S*S
3) If rate is given as per meter – then find perimeter
Hence, Cost = Perimeter * Rate
4) If rate is given as per square meter – then find area
Hence, Cost = Area * Rate
5) No. of tiles (objects) = Area of floor / Area of each tile
—————————————————————————————————————————–
Q.1)Find the area of a rectangle whose length is 25mand breadth is 16m.

SOLUTION: RECTANGLE
Given:
Length = L = 25m
Breadth = B = 16m
Area of rectangle = A = ?

Area of rectangle = L*B

A = 25*16
A = 400sq.m

ANS: Area of rectangle is 400sq.m.
—————————————————————————————————————————–
Q.2) Find the area of square of side 36sq.cm

SOLUTION: SQUARE

Given:
Side = S = 36cm
Area of square = A = ?

Area of square = S*S

A = 36*36
A = 1296sq.cm

ANS: Area of square is 1296sq.cm.
—————————————————————————————————————————–
Q.3) The area of playground is 1,547sq.m. It’s breadth is 17m. What is the length of the playground ?

SOLUTION: RECTANGULAR PLAYGROUND

Given:
Length = L = ?
Breadth = B = 17m
Area of the rectangular playground = A = 1,547sq.m

Area of the rectangular playground = L*B

A = L*17
1,547 = L*17
1,547 / 17 = L
91cm = L

ANS: Area of the rectangular playground is 91sq.cm.
—————————————————————————————————————————–
Q.4) A rectangle and square are equal in area. The side of the square is 24m. If the length of the rectangle is 36m. Find the breadth of the rectangle. Comment on their perimeters.

SOLUTION:

Perimeter of square = 4*S
P = 4*24
P = 96cm

Perimeter of rectangle = 2*( L + B )
P = 2*(36 +16)
P = 2*(52)
P = 104cm

Perimeter of rectangle >Perimeter of square
—————————————————————————————————————————–
Q.5) A drawing room is 5m 40cm long and 4m 10cm wide. How much carpet is required to cover the drawing room ? What will be the cost of the carpet, if 1sq.m of carpet costs Rs.325 ?

SOLUTION: DRAWING ROOM (RECTANGLE)

Given:
Length = L = 5m 40cm = 5.40m
Breadth = B = 4m 10cm = 4.10m
Cost of carpet = ?
Rate of 1sq.m = Rs.325

I) Area of carpet ( rectangle ) = L *B
A = 5.40 *4.40
A = 22.14sq.m

II) Cost – 1sq.m = 325
Total cost – 22.14sq.m = ?
Cost = A * R
= 22.14 * 325
= 7195.5

ANS: Total cost of the carpet is Rs.7195.5.
—————————————————————————————————————————–
Q.6) Find the cost of leveling a ground at the rate of Rs.12 per sq. m. If it is 45m long and 30m wide.

SOLUTION: RECTANGULAR GROUND

Given:
Length = L = 45m
Breadth = B = 30m
Cost of leveling = ?
Rate = Rs.12 per sq. m

I) Area of rectangular ground = L * B
A = 45 *30
A = 1350 sq. m

II) Cost of leveling = Area * Rate
= 1350 * 12
= Rs.16200

ANS: The total cost of leveling is Rs. 16200
—————————————————————————————————————————–
Q.7)Find the cost of fencing a rectangular field 34m 20cm long and 16m 30cm wide at Rs.40 per meter. What will be the cost of turfing it at Rs.21 per meter ?

SOLUTION: RECTANGULAR FIELD

Given:
Length = L = 34m 20cm = 34.20m
Breadth = B = 16m 30cm = 16.30m
Rate of fencing = Rs.40 per meter
Cost of fencing = ?
Rate of turfing = Rs.21 per meter
Cost of turfing = ?

I) Perimeter of rectangle = P = 2*( L + B )
P = 2*(34.20 + 16.30)
P = 2 * 50.5
P = 101.0
P = 101m

Cost of fencing = Perimeter * Rate
= 101 * 40
= Rs. 4040

II) Area = L * B
= 34.20 * 16.30
= 557.46 sq. m

Cost of turfing = Area * Rate
= 557.46 * 21
= Rs.11706.66

ANS: Hence, the total cost of fencing is Rs.11706.66.
—————————————————————————————————————————–
Q.8) What happens to the area of a square if its side is double ?

SOLUTION: SQUARE

Given:
Side = a unit
Area = S * S
A = a * a unit
A = a².

Let side be doubled = 2a unit
A = S*S
A = 2a * 2a
A = 4a².

ANS: If the side of a square is doubled then the area becomes 4 times.
—————————————————————————————————————————–
Q.9) A stick assumed to be 1m long, measured the side of a square field. The area thus calculated was 625 square meter. Later on, it was discovered that the actual length of the stick is 90cm. Find the actual area of the square field.

SOLUTION: SQUARE

Given:
Area = 625 sq. m when length of stick = 1m
Side of square = ?

I) A = S * S
625 = S².
sq root (625) = S
25m = S

But the actual length of stick is 90cm = 0.9m

II) When length of the stick is 1m —————- side of square 25m
When actual length of the stick is 0.9m—————–actual side of the square = ?

Actual side of square = 0.9m * 25
= 22.5m

Actual area of square =S*S
= 22.5 * 22.5
= 506.25 sq. m