# Pythagorean theorem + area of shape - math problems

1. Trapezoid MO The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
2. Garden Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden?
3. Right Δ A right triangle has the length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle.
4. Tetrahedral pyramid What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
5. Triangle SAS Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
6. Square Points A[-9,7] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
7. Rhombus Calculate the perimeter and area of ​​a rhombus whose diagonals are 38 cm and 55 cm long.
8. Rectangle In rectangle with sides, 6 and 3 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
9. Widescreen monitor Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of ​​the LCD monitor with a diagonal size 20 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous tha
10. Triangle Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and itsinterior angles.
11. Prism Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 13 cm has same volume as a cube with an edge length of 3 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube
12. Isosceles right triangle Calculate the area of an isosceles right triangle whose perimeter is 377 cm.
13. Infinity In a square with side 18 is inscribed circle, in circle is inscribed next square, again circle and so on to infinity. Calculate the sum of area of all these squares.
14. R Trapezium Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
15. 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.
16. 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.
17. 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.
18. 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 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.
19. 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 = 22 cm. Calculate: a) the sum of perimeters of all
20. Rhombus 2 Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.

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