1.Calculate the area of a square plot if its diagonal measures 20 meters.
2.Calculate the area of a square field with each side measuring 15 meters.
3.A right-angled triangle has a base measuring 8 units and a hypotenuse of 10 units. What is the area of this triangle?
4.What is the height of an equilateral triangle with each side measuring 2√3 cm?
5.What is the length of a side of an equilateral triangle whose area measures 4√3 cm²?
6.What is the area of a triangle with side lengths of 1 meter, 2 meters, and 3 meters respectively?
7.What is the area of a triangle that has a base measuring 4 meters and a height of 5 meters?
8.Bilal wants to cover his room floor measuring 8 meters by 4 meters with tiles that each measure 25 cm by 20 cm. How many tiles does he require to cover the entire floor?
9.A rectangular plot has one side of 20 feet left open and needs fencing on the remaining three sides. If the total area of the plot is 680 square feet, what is the total length of fencing required?
10.A rectangular piece of land has a length that exceeds its breadth by 20 metres. If fencing this land costs Rs. 5300 at a rate of Rs. 26.50 per metre, what is the length of the land in metres?
11.If the length of a rectangle is reduced to half and its width is increased threefold, what is the resulting percentage change in the area?
12.A rectangle has a length that exceeds its width by 23 meters. If the perimeter measures 206 meters, what is the area of the rectangle?
13.Water is supplied to a tank measuring 200 m by 150 m through a rectangular pipe with dimensions 1.5 m by 1.25 m. If water flows through the pipe at a speed of 20 km/h, how long will it take for the water level in the tank to rise by 2 meters?
14.What is the total surface area of a brick measuring 10 cm by 4 cm by 3 cm?
15.What is equal to the product of the areas of three faces that meet at a corner of a rectangular prism?
16.A cuboid has the sum of its length, width, and height equal to 19 cm, and its diagonal measures 5√5 cm. What is the total surface area of the cuboid?
17.A hall measures 15 meters in length and 12 meters in width. If the combined area of the floor and ceiling equals the total area of the four walls, what is the volume of the hall?
18.A rectangular piece of land measures 240 meters by 180 meters. A 10-meter-wide drain is excavated all around the outside of the land. The soil removed from the drain is evenly spread over the land, raising its surface level by 25 centimeters. What is the depth of the drain?
19.A rectangular pit with dimensions 5 m by 4.5 m by 2.1 m is excavated in the middle of a field that measures 13.5 m by 12.5 m. If the soil removed from the pit is evenly spread over the remaining area of the field, by how much will the ground level rise?
20.A rectangular agricultural plot measures 20 meters in length and 14 meters in width. A pit measuring 6 meters long, 3 meters wide, and 2.5 meters deep is excavated at one corner of the plot. The soil removed from the pit is evenly spread over the remaining area of the field. By how much has the level of the field increased?