Practice problems of the triangle - page 94 of 97
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: 1924
- Rectangular trapezoid
The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid. - Surface of the cone
Calculate the cone's surface if its height is 8 cm and the volume is 301.44 cm³. - Circular sector
I have a circular sector with a length 15 cm with an unknown central angle. It is inscribed by a circle with radius 5 cm. What is the central angle alpha in the circular sector? - Lunes of Hippocrates
Calculate the sum of the area of the so-called Hippocratic lunas, which were cut above the legs of a right triangle (a = 6cm, b = 8cm). Instructions: First, calculate the area of the semicircles above all sides of the ABC triangle. Compare the sum of the - Annulus
Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n. - Find the 13
Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4]. - Angle of two lines
There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV. - Quadrilateral 8405
In the quadrilateral, whose vertices correspond to points 1, 5, 8, and 12 on the dial, calculate the magnitude of the largest inner angle and the deviation of the diagonals. - Truncated pyramid
The concrete pedestal in the shape of a regular quadrilateral truncated pyramid has a height of 12 cm, the pedestal edges have lengths of 2.4 and 1.6 dm. Calculate the surface of the base. - Equilateral triangle v3
Find the area of the colored gray part. An equilateral triangle has a side length of 8 cm. Arc centers are the vertices of a triangle. - Segment
Calculate the segment AB's length if the coordinates of the end vertices are A[10, -4] and B[5, 5]. - Irregular hexagon
There is an irregular hexagon whose sides are the same length. The opposite sides are parallel, and their distance is 237, 195, and193. What is its area? - Quarter circle
What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm? - Spherical cap
The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut. - Hypotenuse 65744
Construct a right triangle ABC with the hypotenuse AB: a) | AB | = 72 mm, | BC | = 51 mm b) | AB | = 58 mm, | AC | = 42 mm - Parallelogram
Find the parallelogram's perimeter, where base a = 8 cm, height v = 3 cm, and angle alpha = 35° is the magnitude of the angle at vertex A. - Two chords
There is a given circle k (center S, radius r). From point A which lies on circle k are starting two chords of length r. What angle does chords make? Draw and measure. - Interior angles
In a quadrilateral ABCD, whose vertices lie on some circle, the angle at vertex A is 58 degrees and the angle at vertex B is 134 degrees. Calculate the sizes of the remaining interior angles. - Tangent
What distance is the tangent t of the circle (S, 4 cm) and the chord of this circle, which is 6 cm long and parallel to the tangent t? - Circumscribed 35781
The regular hexagonal prism is 2 cm high. The radius of the circle circumscribed by the base is 8 cm. Determine its volume and surface.
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