# Pythagorean theorem - examples - page 11

1. ISO trapezoid v2
bases of Isosceles trapezoid measured 12 cm and 5 cm and its perimeter is 21 cm. What is the are of a trapezoid?
2. Base
Compute base of an isosceles triangle, with the arm a=20 cm and a height above the base h=10 cm.
3. Euclidean distance
Calculate the Euclidean distance between shops A, B and C, where: A 45 0.05 B 60 0.05 C 52 0.09 Wherein the first figure is the weight in grams of bread and second figure is price in USD.
4. Vectors
Vector a has coordinates (8; 10) and vector b has coordinates (0; 17). If the vector c = b - a, what is the magnitude of the vector c?
5. TV diagonal
Diagonal TV is 0.56 m long, how big the television sreen is if the aspect ratio is 16:9?
4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
7. Area 4gon
Calculate area of 4-gon, two and the two sides are equal and parallel with lengths 11, 5, 11 and 5. Inner angles are 45°, 135°,45°, 135°.
8. 3sides prism
The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism.
9. Square side
Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0.
10. ISO Triangle V2
Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle.
11. Again saw
From the trunk of the tree we have to a sculpture beam with rectangular cross-section with dimensions 146 mm and 128 mm. What is the trunk smallest diameter?
12. Cube wall
Calculate the cube's diagonal diagonal if you know that the surface of one wall is equal to 36 centimeters square. Please also calculate its volume.
8.3 meters long ladder is leaning against the wall of the well, and its lower end is 1.2 meters from this wall. How high from the bottom of a well is the top edge of the ladder?
14. Pyramid 8
Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
15. Circles
In the circle with a radius 7.5 cm are constructed two parallel chord whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions write both).
16. Triangular pyramid
Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
17. Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
18. Rhombus IV
Calculate the length of the diagonals of the rhombus, whose lengths are in the ratio 1: 2 and a rhombus side is 35 cm.
19. Logs
The log has diameter 30 cm. What's largest beam with a rectangular cross-section can carve from it?