# Right triangle - examples - page 27

1. Quarter circle What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
2. Equilateral triangle A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
3. The perimeter The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX?
4. Rectangular trapezoid The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate trapezium area in cm square and calculate how many differs perimeters of the.
5. Rectangular triangle The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle?
6. Equilateral triangle Calculate the area of an equilateral triangle with circumference 72cm.
7. Coordinate axes Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y.
8. Bamboo Bamboo high 32 feet was at a certain height broken by the wind so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken?
9. Sphere from tree points Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
10. Diagonal to area Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
11. Quadrangular pyramid Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.
12. Find diagonal Find diagonal of cuboid with length=20m width=25m height=150m
13. Ellipse Ellipse is expressed by equation 9x2 + 25y2 - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse.
14. The pond We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
15. Diamond diagonals Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
16. Right triangle Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.
17. Nonagon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
18. Body diagonal Calculate the length of the body diagonal of the 6cm cube.
19. Is right triangle or not If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.
20. Cube diagonals The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.

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