Diagonal + right triangle - math problems

Number of problems found: 201

Diamond area from diagonals
In the diamond ABCD is AB = 4 dm and the length of the diagonal is 6.4 dm long. What is the area of the diamond?
Height of pyramid
The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height?
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.
Height of the cuboid
Cuboid with a rectangular base, measuring 3 cm and 4 cm diagonal has a body 13 centimeters long. What is the height of the cuboid?
Angle of the body diagonals
Using vector dot product calculate the angle of the body diagonals of the cube.
Quadrilateral prism
Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°.
The pyramid 4s
The pyramid with a rectangular base measuring 6 dm and 8 dm has a side edge of length 13 dm. Calculate the surface area and volume of this pyramid.
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?
Construct rhombus
Construct rhombus ABCD if given diagonal length | AC | = 8cm, inscribed circle radius r = 1.5cm
The trapezium
The trapezium is formed by cutting the top of the right-angled isosceles triangle. The base of the trapezium is 10 cm and the top is 5 cm. Find the area of trapezium.
A rhombus
A rhombus has sides of length 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus.
Cuboid face diagonals
The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.
Body diagonal
Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm
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
Wall and body diagonals
Calculate the lengths of the wall and body diagonals of the cuboid with edge dimensions of 0.5 m, 1 m, and 2 m
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?
Area of a rectangle
Calculate a rectangle area with a diagonal of u = 12.5cm and a width of b = 3.5cm. Use the Pythagorean theorem.
Annular area
The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.
Height of the room
Given the floor area of a room as 24 feet by 48 feet and space diagonal of a room as 56 feet. Can you find the height of the room?
Prism 4 sides
The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters