# 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 dm^{2}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 cm^{2}. Calculate the volume of a cone. - Cone

Circular cone of height 15 cm and volume 5699 cm^{3}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. - 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? - 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 cm^{3}. Calculate the surface area of the cylinder. - 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. - 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. - Diameter

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 cm^{3}, a surface of 250 cm^{2}and one side 5 cm long. How do I calculate the remaining sides? - 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? - 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.

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