Diagonal + right triangle - practice problems - page 13 of 21
Number of problems found: 413
- Diagonals
Draw a square ABCD whose diagonals have a length of 6 cm. - Construct rhombus
Construct rhombus ABCD if given diagonal length | AC | = 8 cm, inscribed circle radius r = 1.5 cm - Trapezoid construction
Construct an isosceles trapezoid, whose base is 6 cm long, the base forms an angle of 30 ° with the diagonal, and the arms are 4 cm long. - Construct
Construct a rhombus ABCD with side a = 7 cm, b = 5 cm, whose diagonal e is perpendicular to side b. - Square diagonal construction
There are three different points, C, E, and F, in the plane. Please draw the square ABCD when E and F lie on the diagonals of this square. How many solutions does the task have? - See harmonics
Is it true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. The central segment crosses the intersection of the diagonals and is parallel to the bases. - Construct
Construct a rhombus ABCD if diagonal AC is 6 cm long and diagonal BD is 8 cm long. - Draw a trapezoid
Draw a trapezoid if given a = 7 cm, b = 4 cm, c = 3.5 cm, diagonal AC = 5 cm. Solve as a construction task. - Diagonal of the diamond
The ABCD diamond shape is known as diagonal u2 and a height v. Do an analysis. - Constructing a Square
Construct a square if u-a = 1 - Cardboard box
We want to make an open-top cardboard box in the shape of a quadrilateral prism with a rhombus-shaped base. The rhombus has a side of 5 cm and one diagonal of 8 cm. The height of the box is 12 cm. How many square centimetres of cardboard are needed if ove - Prism + rhomboid
The prism-shaped vessel with a rhomboid base has one base diagonal of 10 cm and the edge of the base 14 cm. The edge of the base and the prism height are in a ratio of 2:5. How many liters of water is in the container when it is filled to four-fifths of t - Billiard balls
A layer of ivory billiard balls radius of 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to everyone adjacent to it. In the spaces between sets of 4 adjacent balls, other balls rest, equal in size to the original. - Wire model
A wire model of a regular hexagonal prism has a base edge length of a = 8 cm and a height of v = 12 cm. The solid is covered with paper — the bases with dark paper and the lateral surface with white paper. - Calculate in cm the greatest possible straight- - Last storm - tree
Mr. Radomír had a misfortune during the last storm; a tree fell on his roof in the shape of a regular four-sided pyramid and destroyed it all. The roof has a base edge length of 8 m and a side edge length of 15 m. How many m² of roofing will he have to bu - Cubes
A sphere is inscribed in one cube and the same sphere is circumscribed about another cube. Calculate the difference between the volumes of the two cubes if the difference between their surface areas is 231 cm². - Box
The cardboard is a box-shaped quadrilateral prism with a rhombic base. Rhombus has a side 5 cm, one diagonal 8 cm long, and the box's height is 12 cm. The package will open at the top. How many cm² of cardboard do we need to cover overlap and joints that - Flowerbed
The flowerbed has the shape of a truncated pyramid. The bottom edge of the base a = 10 m, and the upper base b = 9 m. The deviation angle between the edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be pl - Faces diagonals
Find the cuboid volume if the cuboid's diagonals are x, y, and z (wall diagonals or three faces). Solve for x=1.6, y=1.8, z=1.6 - Hexagon rotation
A regular hexagon of side 6 cm is rotated at 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
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