# Pythagorean theorem - examples - page 23

1. Sphere equation Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
2. Isosceles Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area.
3. Ratio of edges The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
4. Quarter circle What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
5. ABCD square In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?
6. 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.
7. 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?
8. Equilateral triangle Calculate the area of an equilateral triangle with circumference 72cm.
9. 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?
10. 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
11. Diagonal to area Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
12. 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.
13. Find diagonal Find diagonal of cuboid with length=20m width=25m height=150m
14. Body diagonal Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
15. 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.
16. 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?
17. Diamond diagonals Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
18. Nonagon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
19. Body diagonal Calculate the length of the body diagonal of the 6cm cube.
20. Is right triangle or not If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.

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Pythagorean theorem is the base for the right triangle calculator.