# Diagonal + triangle - math problems

#### Number of problems found: 211

• Two circles Two circles with the same radius r = 1 are given. The center of the second circle lies on the circumference of the first. What is the area of a square inscribed in the intersection of given circles?
• Circular ring Square with area 16 centimeters square are inscribed circle k1 and described circle k2. Calculate the area of circular ring, which circles k1, k2 form.
• Logs The trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
• Cuboidal room Length of cuboidal room is 2m breadth of cuboidal room is 3m and height is 6m find the length of the longest rod that can be fitted in the room
• The diagonals The diagonals of the KOSA diamond are 20 cm and 48 cm long. Calculate the circumference of the diamond in centimeters rounded to one unit.
• Regular hexagonal prism Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.
• Sphere and cone Within the sphere of radius G = 33 cm inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone?
• Prism The lenght, width and height of a right prism are 17, 11 and 11 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
• Rhombus ABCD Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.
• Rhombus Calculate the perimeter and area of ​​a rhombus whose diagonals are 39 cm and 51 cm long.
• Rhomboid The dimensions of the rhomboid sides are a= 5cm, b = 6 cm and the size of the angle at the vertex A is 60°. What is the length of side AC?
• See harmonics It is true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. Central segment crosses the intersection of the diagonals and is parallel to the bases.
• Wall and body diagonals The block/cuboid has dimensions a = 4cm, b = 3cm and c = 12cm. Calculates the length of the wall and body diagonals.
• Construct rhombus Construct rhombus ABCD if given diagonal length | AC | = 8cm, inscribed circle radius r = 1.5cm
• Two diagonals The diagonals of the diamond EFGH have lengths in the ratio 1: 2. What is the circumference of a rhombus if the longer of the diagonals is 8 cm long?
• Tree trunk From the tree trunk, the diameter at the narrower end is 28 cm, a beam of square cross-section is to be made. Calculate the longest side of the largest possible square cross-section.
• Company logo The company logo consists of a blue circle with a radius of 4 cm, which is an inscribed white square. What is the area of the blue part of the logo?
• Forces Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant?
• 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
• Diagonals of the rhombus How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm2?

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