Pythagorean theorem - problems - page 4

1. Triangle
Can be rectangular triangle equilateral?
2. R Trapezium
Rectangular trapezium has bases 18 and 11 and area 28 cm2. What is its perimeter?
3. Octagon
We have a square with side 84 cm. We cut the corners to make his octagon. What will be the side of the octagon?
4. Cube - angles
Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base.
5. Cap
Jesters hat is shaped a rotating cone. Calculate how much paper is needed to the cap 60 cm high when head circumference is 52 cm.
6. Pyramid roof
1/3 of area of ​​the roof shaped regular tetrahedral pyramid with base edge 9 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered?
7. Sphere slices
Calculate volume and surface of a sphere, if the radii of parallel cuts r1=31 cm, r2=92 cm and its distance v=25 cm.
8. Rhombus
Find the length of the other diagonal and area of rhombus. The perimeter of a rhombus is 40 cm and one of the diagonals is of length 10 cm.
9. Climb
On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went?
10. Tetrahedral pyramid
Calculate the volume and surface area of a regular tetrahedral pyramid, its height is \$b cm and the length of the edges of the base is 6 cm.
11. ISO triangle
Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.
12. 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 39 degrees, |AB| = 3 cm. Calculate the volume of the prism.
13. Recursion squares
In the square ABCD is inscribed a square so that its vertices lie at the centers of the sides of the square ABCD.The procedure of inscribing square is repeated this way. Side length of square ABCD is a = 42 cm. Calculate: a) the sum of perimeters of all
14. Diagonals of the rhombus
Calculate height of rhombus whose diagonals are 12 cm and 19 cm.
15. Rhombus 2
Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
16. Leg and height
Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m.
17. Similarity coefficient
The ratio of similarity of two equilateral triangles is 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of ​​the larger triangle.
18. Regular quadrangular pyramid
How many square meters is needed to cover the tower the shape of regular quadrangular pyramid base edge 10 meters, if the deviation lateral edges from the base plane is 68 °? Calculate coverage waste 10%.
19. Axial section
Axial section of the cylinder has a diagonal 31 cm long and we know that the area of the side and the area of base is in ratio 3:2. Calculate the height and radius of the cylinder base.
20. Pyramid - angle
Calculate the surface of regular quadrangular pyramid whose base edge measured 6 cm and the deviation from the plane of the side wall plane of the base is 50 degrees.

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Pythagorean theorem is the base for the right triangle calculator.