# Area + expression of a variable from formula - examples

1. 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.
2. 3rd dimension
The block has a surface of 42 dm2 and its dimensions are 3 dm and 2 dm. What is the third dimension?
3. Right Δ
Right triangle has length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
4. 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.
5. 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.
6. Right isosceles
Calculate area of the isosceles right triangle which perimeter is 41 cm.
7. Garden
Trapezoid garden has parallel sides 19 m and 24 m. Its area is 193.5 square meters. What is the width of the garden?
8. 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.
9. Equilateral cylinder
Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
10. Vintner
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.
11. Above Earth
To what height must a boy be raised above the earth in order to see one-fifth of its surface.
12. Rhombus diagonal
Area of rhombus is 224. One diagonal measures 33, find length of other diagonal.
13. Diameter
What is the inside diameter of the cylinder container and if half a liter of water reaches a height 15 cm?
14. 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.
15. 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?
16. Glass
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?
17. 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.
18. 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
19. Cube 5
The content area of one cube wall is 32 square centimeters. Determine the length of its edges, its surface and volume.
20. Cube wall
The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube.

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