# Triangle - math word problems

1. ISO trapezoid v2 bases of Isosceles trapezoid measured 12 cm and 5 cm and its perimeter is 21 cm. What is the are of a trapezoid?
2. Triangular prism The base perpendicular triangular prism is a right triangle whose hypotenuse measures 5 cm and one cathetus 2 cm. Height of the prism is equal to 7/9 of the perimeter of the base. Calculate the surface area of prism.
3. Sphere - parts Calculate the area of a spherical cap, which is part of an area with base radius ρ = 9 cm and a height v = 3.1 cm.
4. Acute angles Sizes of acute angles in the right-angled triangle are in the ratio 1: 3. What is size of the larger of them?
5. Climb in percentage The height difference between points A and B is 475 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 7.4 km.
6. Climb For horizontal distance 4.2 km road rise by 6.3 m. Calculate the road pitch in ‰ (permille, parts per thousand).
7. Sphere and cone Within the sphere of radius G = 33 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
8. Hexagon 5 The distance of parallel sides of regular hexagonal is 61 cm. Calculate the length of the radius of the circle described to this hexagon.
9. Pentagonal pyramid Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 7.7 cm and a plane ABV, ABC has angle 37 degrees.
10. Triangular prism Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.
11. Cosine The point (8, 6) is on the terminal side of angle θ. cos θ = ?
12. Catheti The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs. In the square ABCD point P is in the middle of the DC side and point Q in the middle pages AD. If the area of quadrilateral BQPC is 49 cm2, what is the area of ABCD?
14. 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.
15. Sails We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
16. Park In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
17. KLMN In the trapezoid KLMN is given this informations: 1. segments KL and MN are parallel 2. segments KL and KM has same length 3. segments KN, NM and ML has same length. Determine the size of the angle KMN.
18. RT 11 Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long. 8.3 meters long ladder is leaning against the wall of the well, and its lower end is 1.2 meters from this wall. How high from the bottom of a well is the top edge of the ladder?
20. Diamond Rhombus has side 17 cm and and one of diagonal 22 cm long. Calculate its area.

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