# Right triangle - 8th grade (13y) - examples - page 8

1. OPT What is the perimerer of a right triangle with the cathetuses 16 cm and 14 cm?
2. 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.
3. Rhombus Calculate the length of the diagonal AC of the rhombus ABCD, if its perimeter is 84 dm and the other diagonal BD has length 20 dm.
4. Prism - box The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm3. Calculate the surface of the prism.
5. Semicircle In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
6. Sun rays If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current hei
7. Vertical prism The base of vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism
8. Common chord Two circles with radius 17 cm and 20 cm are intersect at two points. Its common chord is long 27 cm. What is the distance of the centers of these circles?
9. Leg Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg.
10. Chord AB What is the length of the chord AB if its distance from the center S of the circle k(S, 92 cm) is 10 cm?
11. Isosceles trapezoid The lengths of the bases of the isosceles trapezoid are in the ratio 5:3, the arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid.
12. Trapezoid RT The plot has a shape of a rectangular trapezium ABCD, where ABIICD with a right angle at the vertex B. side AB has a length 36 m. The lengths of the sides AB and BC are in the ratio 12:7. Lengths of the sides AB and CD are a ratio 3:2. Calculate consumptio
13. Rectangular trapezoid The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid.
14. Triangle Calculate the sides of the triangle if its area S = 630 and the second cathethus is shorter by 17.
15. Cube - wall V kocke ABCDEFGH je ?. Aký je povrch kocky?
16. Complete construction Construct triangle ABC if hypotenuse c = 7 cm and angle ABC = 30 degrees. / Use Thales' theorem - circle /. Measure and write down the length of legs.
17. RT 11 Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
18. IS trapezoid Isosceles trapezoid arm measured 35 cm. Height is 30 cm and middle segment is 65 cm. Determine length of its bases.
19. Estate Estate shaped rectangular trapezoid has bases long 34 m , 63 m and perpendicular arm 37 m. Calculate how long is its fence.
20. Diamond ABCD In the diamond ABCD is the diagonal e = 24 cm and size of angle SAB is 28 degrees, where S is the intersection of the diagonals. Calculate the circumference of the diamond.

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