Solved Area Problems

Solved Area Problems

Dear Reader,
Below are four problems dealing with area of square and rectangles.

Question 1

The number of tiles of length 60 cm and breadth 40 cm were needed to pave the floor of a square room of length 6 meters is:

a) 120 b) 140 c) 150 d) 159

Answer : c) 150.

Solution :

Length of the floor = 6 m = 600 cm
Area of the floor = 600² x m² = 600 x 600 cm²

Length of each tile = 60 cm and breadth = 40cm
Area of each tile = 60 x 40 cm²

Number of tiles required to pave the floor = area of the floor / area of each tile
= 600 x 600 / 40 x 60 = 3600 / 24 = 150.

Question 2

If 100 square marbles of equal size were required to pave a floor of dimension 6m x 24m then the length of each marble is:

a) 120 cm b) 144 cm c) 250cm d) 100 cm

Answer : a) 120 cm.

Solution :

Dimension of the floor = 6m x 24 m
Area of the floor = 6 x 24 m².

It is given that, 100 square marbles are needed to cover the floor of area 6 x 24 m².

Area of each marble = 6 x 24 / 100 m²= 144 / 100 m² = 1.44 m²

Since the marbles are in square shape, the length of each marble = sqrt(1.44) m = 1.2 m

Hence the answer is 1.2m = 1.2 x 100 cm = 120 cm.

Question 3

A man want to pave the floor of a room of length 30m 34 cm and 18m 4cm breadth; the minimum number of square marbles needed for him is:

a) 922 b) 291 c) 814 d) 628

Answer : c) 814

Solution :

Length of the room = 30m and 34 cm = 30 x 100 + 34 cm = 3034 cm
And, breadth = 18 m and 4 cm = 18 x 100 + 4 cm = 1804 cm

We have to find minimum number of marbles; so, the length of each marble will be the possible largest unit.

Length of largest marble = HCF (3034, 1804) cm = 82 cm.

Area of each marble = 82 x 82 cm².
Now, the required number of marbles = area of the floor / area of each tile = (3034 x 1804) / (82 x 82) = 814.

Hence the required number of marbles = 814.

Question 4

The dimension of a rectangular floor of a room is 10m x 5m. The owner want to pave the floor by equal number of 2 different color square marbles of length 1m. If he uses green and white color marbles then the number of green color marbles is:

a) 50 b) 25 c)100 d) 75

Answer : b) 25.

Solution :

Dimension of the floor = 10m x 5m

Area of the floor = 5 x 10 m² = 50m².

Length of each square marble = 1 m
Then its area = 1 m².

Total number of green and white color marbles = Area of the floor / area of each marble
= 50/1 = 50

Number of green color marbles required = 50/2 = 25.