Unit conversion + square (second power, quadratic) - practice problems - last page
Number of problems found: 458
- Quadrilateral 81097
The quadrilateral ABCD is symmetrical about the diagonal AC. The length of AC is 12 cm, the length of BC is 6 cm, and the interior angle at vertex B is right. points E and F are given on the sides AB, and AD so that the triangle ECF is equilateral. Determ - Quadrilateral 82146
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. - Corresponding 6021
How much paint do we need to paint a pool in the shape of a 6-sided prism? The base edge measures 21 dm, the corresponding height is 1.8 m, and the pool height is 150 cm. We need 0.21 kg of paint per 1 m². - Establish 72234
How many kg of grass seed should be bought to establish a lawn around a circular fountain with a diameter of 5 m if the lawn is to be 1.5 m wide and 1 g of grass seed is used per 1 dm of the square area?
- Truncated pyramid
The concrete pedestal in 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. - A rhombus 4
A rhombus has a side length of 10 cm. Find the angles at each corner of the rhombus if the shorter of the two diagonals measures 7 cm. Give your answers to the nearest degree and give clear geometric reasoning at each stage of your solution. - Archaeologists 81478
Archaeologists need to find out the size of the vessel if the sherd found was in the shape of a circular section with a length of 12 cm and a height of 3 cm. What is the area of this section? - Inaccessible 69794
Determine the distance between two inaccessible places P, Q, if the distance between two observation points A, B is 2000m and if you know the size of the angles QAB = 52°40''; PBA = 42°01''; PAB = 86°40'' and QBA = 81°15''. The considered locations A, B, - Diagonals in diamond
In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
- Around
Around the circular flowerbed with a radius of 2 m is a sidewalk 80 cm wide. How many square meters does the sidewalk have? - Circle arc
Calculate the circular arc area in m² where the diameter is 263 dm and a central angle is 40°. Please result round to three decimal places. - Circular 82418
A circular segment has an area of 6.04 cm², the central omega angle is 15 degrees, what is the radius? - 4side pyramid
Calculate the volume and surface of the regular four-sided pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees. - Square equal rhombus
Construct a square that has the same area as a rhombus ABCD if |AB| = 5cm, |AD| = 4cm and angle |DAB| = 30°.
- Perimeter 83352
A circle with a diameter of 30 cm is cut by a chord t = 16 cm. Calculate the perimeter and area of the smaller segment. - Circular segment
Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm, and the angle α = 60°. Help formula: S = 1/2 r². (Β-sinβ) - Parallelogram
Calculate area of the parallelogram ABCD as shown if |AB| = 13 cm, |BC| = 99 cm and angle BAD = 100° - Cylinder horizontally
The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the cylinder's axis. How many hectoliters of water is in the cylinder?
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