# Pythagorean theorem - examples - page 26

1. Square
Calculate the area of the square shape of the isosceles triangle with the arms 50m and the base 60m. How many tiles are used to pave the square if the area of one tile is 25 dm2?
2. Waste
How many percents are waste from a circular plate with a radius of 1 m from which we cut a square with the highest area?
3. A truck
A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
Adam placed the ladder of the house, the upper end reaching to the window at the height of 3.6m, and the lower end standing on level ground and was distant from a wall of 1.5m. What is the length of the ladder?
5. Pavement
Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m.
6. Spherical cap
Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm2. Determine the radius r of the sphere from which the spherical cap was cut.
7. Cube cut
The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '.
8. Three points
Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
9. Distance of lines
Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm
10. Spruce height
How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?
11. Tetrahedral pyramid
Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m.
12. A box
A box is 15 centimeters long, 4 centimeters wide, and 3 centimeters tall what is the diagonal S of the bottom side? What is the length of the body diagnol R?
13. Isosceles trapezoid
The old father decided to change the top plate of an isosceles-like trapezoid with the basic dimensions of 120 cm and 60 cm, and the shoulder is 50 centimeters long. How much does it pay for a new plate and a square meter worth 17 euros?
14. Infinite sum of areas
Above the height of the equilateral triangle ABC is constructed an equilateral triangle A1, B1, C1, of the height of the equilateral triangle built A2, B2, C2, and so on. The procedure is repeated continuously. What is the total sum of the areas of all tri
15. Right triangular prism
We have cuboid with a base and dimensions of 12 cm and 5 cm and height of 4 cm. The tablecloth cut it into two identical triangular prisms with right triangular bases. The surface of the created prisms was painted with color. Calculate the surface area of.
16. KLM triangle
Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees.
17. Circle annulus
There are 2 concentric circles in the figure. Chord of larger circle 10 cm long is tangent to the smaller circle. What are does annulus have?
18. Bricklayer
How much do we pay for a bricklayer laying a pavement in a square room with a diagonal of 8 m, if 1 sqm with work will cost for CZK 420?
19. Center of line segment
Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .
20. Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor and

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Pythagorean theorem is the base for the right triangle calculator.