Practice problems of the right triangle - page 74 of 82
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). This angle is formed by the intersection of two of the triangle's sides, which are called the legs of the triangle. The other side of the triangle is called the hypotenuse, which is the side opposite the right angle, and is the longest side of the triangle. Right triangles are important in mathematics and are used in many areas of science and engineering, including trigonometry, physics, and construction. The Pythagorean theorem which states that in a right triangle, the sum of the squares of the legs (a,b) equals the square of the hypotenuse (c) is a fundamental result in geometry.Number of problems found: 1624
- Right trapezoid
The right trapezoid has bases 3.2 cm and 62 mm long. The shorter leg has a length of 0.25 dm. Calculate the lengths of the diagonals and the second leg. - Circumscribed 7290
Calculate the area of a regular hexagon if the radius of the circle circumscribed is 6.8 cm. - 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 are 10 cm. - Quadrilateral 6332
The regular quadrilateral pyramid is 2 m high. The height of the sidewall is 2.8 m. What are the dimensions of the base? Calculate the surface area and volume of the pyramid.
- Regular quadrilateral pyramid
What is the volume of a regular quadrilateral pyramid if its surface is 576 cm² and the base edge is 16 cm? - Diagonals of the rhombus
How long are the diagonals e, and f in the diamond if its side is 5 cm long and its area is 20 cm²? - 9-gon pyramid
Calculate a nine-sided pyramid's volume and surface, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm. - Vertices of a right triangle
Show that the points D(2,1), E(4,0), and F(5,7) are vertices of a right triangle. - Quadrilateral 8220
Calculate the volume of a regular quadrilateral pyramid, whose wall height is w = 12 cm and the edge of the base is a = 5 cm.
- Nine-sided 36071
Calculate the surface area and volume of a regular nine-sided pyramid if the radius of the circle inscribed in the base measures ρ = 12 cm and the height of the pyramid is 24 cm - Triangular prism
Calculate a triangular prism if it has a rectangular triangle base with a = 4cm and hypotenuse c = 50mm, and the height of the prism is 0.12 dm. - Concentric circles and chord
In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius has the concentric circle while touching this chord? - Chord
In a circle with a radius r=60 cm is the chord, 4× longer than its distance from the center. What is the length of the chord? - The plaster cast
The plaster cast has the shape of a regular quadrilateral pyramid. The cover consists of four equilateral triangles with a 5 m side. Calculate its volume and surface area.
- Parallelogram 5027
Calculate the area of the parallelogram if the side sizes are a = 80, b = 60, and the size of the diagonal angle is 60°. - 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? - Determine 6415
Determine the distance of two parallel chords of lengths of 7 cm and 11 cm in a circle with a radius of 7 cm. - Quadrilateral 69834
What is the volume of a regular quadrilateral pyramid? The pyramid height is 30 cm, and the wall height is 50 cm. - Quadrilateral 32193
In a regular quadrilateral pyramid, the base edge a = 6cm, the side edge b = 10cm. Calculate the height of the pyramid.
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