Area + expression of a variable from formula - examples
- The sides 2
The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
- 3rd dimension
The block has a surface of 42 dm2 and its dimensions are 3 dm and 2 dm. What is the third dimension?
- Right Δ
Right triangle has length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
- Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
Circular cone of height 15 cm and volume 5699 cm3 is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
- Right isosceles
Calculate area of the isosceles right triangle which perimeter is 41 cm.
Trapezoid garden has parallel sides 19 m and 24 m. Its area is 193.5 square meters. What is the width of the garden?
- Cone and the ratio
Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
- Equilateral cylinder
Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
How high can vintner fill keg with crushed red grapes if these grapes occupy a volume of 20 percent? Keg is cylindrical with a diameter of the base 1 m and a volume 9.42 hl. Start from the premise that says that fermentation will fill the keg (the number.
- Above Earth
To what height must a boy be raised above the earth in order to see one-fifth of its surface.
- Rhombus diagonal
Area of rhombus is 224. One diagonal measures 33, find length of other diagonal.
What is the inside diameter of the cylinder container and if half a liter of water reaches a height 15 cm?
- Tetrahedral prism - rhomboid base
Calculate the area and volume tetrahedral prism that has base rhomboid shape and its dimensions are: a = 12 cm, b = 70 mm, v_a = 6 cm, v_h = 1 dm.
- Cuboid - volume and areas
The cuboid has a volume of 250 cm3, a surface of 250 cm2 and one side 5 cm long. How do I calculate the remaining sides?
How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?
- Square vs rectangle
Square and rectangle have the same area contents. The length of the rectangle is 9 greater and width 6 less than side of the square. Calculate the side of a square.
- Trapezoid 15
Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4
- Cube 5
The content area of one cube wall is 32 square centimeters. Determine the length of its edges, its surface and volume.
- Cube wall
The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube.