Triangle practice problems - page 112 of 126
Number of problems found: 2502
- Rhombus
It is given a rhombus with a side length of a = 20 cm. Touchpoints of the inscribed circle divided its sides into sections a1 = 13 cm and a2 = 7 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Arch ground length
The arch has a radius of 3.3 m, a span of 3.25 m, and a height of 20 cm above the ground. What is the length of the arc to reach the ground? - Digging a pit
The pit has the shape of a regular quadrilateral truncated pyramid. The edges of the bases are 14m and 10m long. The sidewalls form an angle of 135° with a smaller base. Find how many m³ of soil were excavated when digging the pit. - Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base of 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure. - Quadrilaterals II
In the ABCDEFGHIJKL, the two adjacent sides are perpendicular to each other, and all sides except the AL and GF sides are identical. The AL and GF sides are twice as long as the other sides. The lines BG and EL intersect at point M and divide the dodecago - Circle length
The 16 cm long string is 6 cm from the circle's center. Calculate the length of the circle. - Annulus from triangle
Calculate the area of the area bounded by a circle circumscribed and a circle inscribed by a triangle with sides a = 25mm, b = 29mm, c = 36mm. - Inscribed triangle
A circle is an inscribed triangle, and its vertices divide the circle into three arcs. The length of the arcs is in the ratio 2:3:7. Find the interior angles of a triangle. - The bus stop
The bus stop waiting room has the shape of a regular quadrilateral pyramid 4 m high with a 5 m base edge. Calculate how much m² roofing is required to cover the sheathing of three walls, taking 40% of the additional coverage. - Tetrahedral pyramid
Calculate the regular tetrahedral pyramid's volume and surface if the area of the base is 20 cm² and the deviation angle of the side edges from the plane of the base is 60 degrees. - A kite
ABCD is a kite. Angle OBC = 20° and angle OCD = 35°. O is the intersection of diagonals. Find angle ABC, angle ADC, and angle BAD. - Chord circle length
The chord AB is in the circle k with a radius of 13 cm. The center C of the string AB is 5 cm from the center S of the circle. How long is the AB string? - Quadrilateral prism
Calculate the volume and surface area of a regular quadrilateral prism with base edge a=24 cm if the body diagonal makes an angle of 66° with the base. - Quadrilateral prism
The height of a regular quadrilateral prism is v = 10 cm, and the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the prism's volume. - Octagon from rectangle
We cut the corners of a rectangular tablecloth with dimensions of 4 dm and 8 dm into isosceles triangles. Thus, the octagon formed had an area of 26 dm². How many dm² of tablecloth do we cut down? - Rhombus and inscribed circle
It is given a rhombus with side a = 6 cm and the inscribed circle r = 2 cm radius. Calculate the length of its two diagonals. - Central angle
A circle k with a center at point S and a radius of 6 cm is given. Calculate the size of the central angle subtended by a chord 10 cm long. - 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°. - Regular quadrangular pyramid
How many square meters are needed to cover the shape of a regular quadrangular pyramid base edge of 10 meters if the deviation lateral edges from the base plane are 68°? Calculate waste 10%. - Rhombus base
Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u1 = 17 cm and u2 = 14 cm. The prism height is twice the base edge length.
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