Geometry And Mensuration Quiz

1) A flooring tile had the shape of a parallelogram whose base is 24cm and the corresponding height is 10cm. How many such tiles are required to cover the floor of area 1080m2?

45000 tiles

35000 tiles

48000 tiles

40000 tiles

To find the number of tiles required, we first need to calculate the area of one tile, which is base x height = 24cm x 10cm = 240cm^2. Next, convert the total area to cm^2: 1080m^2 x 10000 = 10800000cm^2. Finally, divide the total area by the area of one tile to get the number of tiles needed: (10800000cm^2) / (240cm^2) = 45000 tiles.

Explanation

To find the number of tiles required, we first need to calculate the area of one tile, which is base x height = 24cm x 10cm = 240cm^2. Next, convert the total area to cm^2: 1080m^2 x 10000 = 10800000cm^2. Finally, divide the total area by the area of one tile to get the number of tiles needed: (10800000cm^2) / (240cm^2) = 45000 tiles.

2) A room is 7m long and 5m broad. It has one door measuring 2m by 1.5m and two windows each measuring 1.5m x 1m. The cost of painting the walls at Rs 12.50 per Sqm is Rs 825. Find the height of the room.

2.5m

3m

3.5m

4m

To find the height of the room, we need to consider the total area of the walls to be painted. Subtract the area of the door and windows from the total wall area. Then divide the remaining area by the perimeter of the room to find the height. In this case, the correct calculation leads to a height of 3 meters.

Explanation

To find the height of the room, we need to consider the total area of the walls to be painted. Subtract the area of the door and windows from the total wall area. Then divide the remaining area by the perimeter of the room to find the height. In this case, the correct calculation leads to a height of 3 meters.

3) The base of a ||gm is three times its height. If the area is 867 cm2, find the base and height of the ||gm.

102 cm

68 cm

34 cm

51 cm

To find the base and height of a parallelogram, we can use the formula: Area = base * height. Since we are given that the base is three times the height, we can set up the equation as 3h * h = 867. Solving for h gives h = 17. Therefore, the height is 17 cm and the base is 51 cm.

Explanation

To find the base and height of a parallelogram, we can use the formula: Area = base * height. Since we are given that the base is three times the height, we can set up the equation as 3h * h = 867. Solving for h gives h = 17. Therefore, the height is 17 cm and the base is 51 cm.

4) Find the area of a rhombus having each side equal to 13 cm and one of its diagonal is 24 cm.

120 cm2

156 cm^2

96 cm^2

85 cm^2

To find the area of a rhombus, we can use the formula (d1 * d2) / 2, where d1 and d2 are the diagonals. In this case, the diagonals are 24 cm and 2 * sqrt(13^2 - 12^2) = 2 * 5 = 10 cm. Thus, the area will be (24 * 10) / 2 = 240 / 2 = 120 cm^2.

Explanation

To find the area of a rhombus, we can use the formula (d1 * d2) / 2, where d1 and d2 are the diagonals. In this case, the diagonals are 24 cm and 2 * sqrt(13^2 - 12^2) = 2 * 5 = 10 cm. Thus, the area will be (24 * 10) / 2 = 240 / 2 = 120 cm^2.

5) Find the area of the shaded region ABCD in a square with 2 semicircles?

35 cm2

42 cm2

50 cm2

28 cm2

To find the area of the shaded region, start by calculating the area of the square (side x side). Then, subtract the combined area of the two semicircles. Finally, you will arrive at the area of 42 cm2.

Explanation

To find the area of the shaded region, start by calculating the area of the square (side x side). Then, subtract the combined area of the two semicircles. Finally, you will arrive at the area of 42 cm2.

6) The diameter of a wheel of a bus is 90 cm which makes 315 revolution per minute. Determine its speed in km per hour.

68.72 km/hr

53.46 km/hr

41.89 km/hr

27.25 km/hr

To calculate the speed of the bus, first find the circumference of the wheel using the formula C = πd. Then, the distance covered in one minute is the product of circumference and number of revolutions. Convert the distance to km and time to hours to get the speed.

Explanation

To calculate the speed of the bus, first find the circumference of the wheel using the formula C = πd. Then, the distance covered in one minute is the product of circumference and number of revolutions. Convert the distance to km and time to hours to get the speed.

Geometry and Mensuration Quiz