# The most difficult examples - page 5

1. Pyramid Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC.
2. Two triangles SSA Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14
3. Isosceles trapezoid Perimeter of the isosceles trapezoid is 48 cm. One side is two times greater than the second side. Determine the dimensions of the trapezoid.
4. Metal box How much metal we need for the production of box with dimensions 5 dm, 30 cm and a height of 1 m? Add 12% of the waste and folds.
5. Reducing scale I am sizing some landscaping and I measured everything for a 20 to 1 scale. I realized when I was done that it was at 30 to 1. How can I convert what I already have to 30 to 1. (Example, grass area is 22,871.6' at 20 to 1, how do you figure it out to be 30
6. Diagonals of diamond Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.
7. Chord - TS The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS?
8. Prism Find the volume and surface area of prism with base of an equilateral triangle with side 7 dm long and the body height of 1.5 m.
9. The tram The tram is moving with acceleration a = 0.3m/s2. How long it will pass the first meter of track? How long does it take 10 meters. What is its speed at the end of the 10 meters track?
10. Cone container Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
11. 3d vector component The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
12. Linear imaginary equation Given that ? "this is z star" Find the value of the complex number z.
13. Geometric sequence 5 About members of geometric sequence we know: ? ? Calculate a1 (first member) and q (common ratio or q-coefficient)
14. Hexagon area The center of the regular hexagon is 21 cm away from its side. Calculate the hexagon side and its area.
15. Evaluate expression Evaluate expression using BODMAS rule: 1 1/4+1 1/5÷3/5-5/8
16. Resultant force Calculate mathematically and graphically the resultant of a three forces with a common centre if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
17. Ten fractions Write ten fractions between 1/3 and 2/3
18. 30-gon At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
19. Math logic There are 20 children in the group, each two children have a different name. Alena and John are among them. How many ways can we choose 8 children to be among the selected A) was John B) was John and Alena C) at least one was Alena, John D) maximum one w
20. Goniometric form Determine goniometric form of a complex number ?.

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