Area of shape + expression of a variable from formula - math problems

1. Base of prism The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm2.
2. Right Δ A right triangle has the length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle.
3. Tereza The cube has area of base 256 mm2. Calculate the edge length, volume and area of its surface.
4. R Trapezium Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
5. Arc and segment Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 33 and corresponding angle is ?.
6. ISO triangle Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.
7. Rhombus 2 Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
8. Circle How big is area of circle if its circumference is 80.6 cm?
9. Right isosceles Calculate area of the isosceles right triangle which perimeter is 41 cm.
10. 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?
11. Right triangle Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
12. Perimeter and legs Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
13. 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.
14. Trapezoid trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area?
15. Cathethus and the inscribed circle In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.
16. Rectangle diagonals It is given rectangle with area 24 cm2 a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
17. Equilateral cylinder Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
18. Rectangle The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle.
19. 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.
20. Triangular pyramid It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm3. What is it content (surface area)?

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