Practice problems of the triangle - page 93 of 116
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. The sum of the measures of the interior angles of a triangle is always 180 degrees. An exterior angle of a triangle is an angle that is a linear pair (and hence supplementary) to an interior angle. The best known area formula is T = a*h /2 where a is the length of the side of the triangle, and h is the height or altitude of the triangle.Number of problems found: 2320
- Diagonals of pentagon
Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm. - Hexagon 5
The distance of parallel sides of regular hexagonal is 61 cm. Calculate the length of the radius of the circle described in this hexagon. - Hexagon A
Calculate the area of a regular hexagon inscribed in a circle with radius r=9 cm. - Determine 82032
Determine the volume and surface area of a cone whose slope of length 8 cm makes an angle of 75 degrees with the plane of the base. - Pentagonal pyramid
The height of a regular pentagonal pyramid is as long as the edge of the base, 20 cm. Calculate the volume and surface area of the pyramid. - Hexagonal prism
The prism's base is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Find the volume and surface of the prism. - An equilateral cone
Determine the radius and height (in centimeters) of an equilateral cone that has a volume of 1 liter. - Vectors
Find the magnitude of the angle between two vectors u = (3; -5) and v = (10; 6) - Circumscribed 2671
The circle's radius circumscribed by the rectangle is 5 cm, and one side of the rectangle is 6 cm long. Calculate the length of the other side and the area of the rectangle. - Circumscribed 63824
In a regular decagon, the diameter of the circumscribed circle measures 10 cm. Determine the radius of the circle inscribed in this triangle. - Inscribed 43991
An irregular convex octagon is inscribed in the circle. Its four adjacent sides have a length of 3, and the remaining four adjacent sides have a size of 2. What is the area of a given octagon? - Railway
Railway line had on 5.8 km segment climb nine permille. How many meters does the track ascent? - Calculate 5115
In the rotating cylinder, it is given: V = 120 cm3, v = 4 cm. Calculate r, S mantle. - N-gon II
What is the side length of the regular 9-gon circumscribed circle of radius 13 cm? - Traffic cones
Forty identical traffic cones with a base diameter d = 3 dm and a height v = 6 dm should be painted on the outside with orange paint (without base). How many crowns do we pay for color? If we need 50 cm³ of paint to paint, 1m² and 1l of paint cost CZK 80? - Calculate 23411
The prism with a diamond base has one base diagonal of 20 cm and a base edge of 26 cm. The edge of the base is 2:3 to the height of the prism. Calculate the volume of the prism. - Octagonal pyramid
Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the base plane is α = 60°. - Decagon prism
A regular decagon of side a = 2 cm is the base of the perpendicular prism. The side walls are squares. Find the prism volume in cm³, round to two decimal places. - Belongs 8412
Given a circle k(O; 2.5 cm), a line p: /Op/=4 cm, a point T: T belongs to p and at the same time /OT/=4.5 cm. We must find all the circles that will touch the circle k and the line p at point T. - Inscribed and described circle
Find the radii of a circle inscribed and circumscribed by a regular pentagon whose side measures 3 cm.
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