# Diagonal + triangle - math problems

#### Number of problems found: 212

• Rhombus diagonals In the rhombus ABCD are given the sizes of diagonals e = 24 cm; f = 10 cm. Calculate the side length of the diamond and the size of the angles, calculate the content of the diamond
• Tetrahedral pyramid It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
• 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
• Angle of the body diagonals Using vector dot product calculate the angle of the body diagonals of the cube.
• MO Z8–I–6 2018 In the KLMN trapeze, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line.
• Diagonals at right angle In the trapezoid ABCD, this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD?
• Regular hexagonal prism Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.
• Square pyramid Calculate the pyramid's volume with the side 5cm long and with a square base, side-base has an angle of 60 degrees.
• Faces diagonals If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), then find the cuboid volume. Solve for x=1.3, y=1, z=1.2
• Ratio of sides Calculate the area of a circle with the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
• Draw a trapezoid Draw a trapezoid if given a = 7 cm, b = 4 cm, c = 3.5 cm, diagonal AC = 5cm. Solve as a construction task.
• Diamond diagonals Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square, and the side length is 13 cm.
• Distance of points A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S.
• Central park in city The city park has the shape of a rectangle of 180 meters in length and 120 meters in width. People make their walk through the center of the park from one corner to the second. Calculate how many meters this way is shorter than they walked along the path
• Rhombus and inscribed circle It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
• Rhombus It is given a rhombus of side length a = 19 cm. Touchpoints of inscribed circle divided his sides into sections a1 = 5 cm and a2 = 14 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
• Support colum Calculate the volume and surface of the support column that is shaped as perpendicular quadrangular prism whose base is a rhombus with a diagonals u1 = 102 cm u2 = 64 cm. Column height is 1. 5m.
• Rectangle The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle.
• Total area Calculate the total area (surface and bases) of a prism whose base is a rhombus which diagonals of 12cm and 18cm and prism height is 10 cm.
• Forces In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N, and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2, and F3.

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