Planimetrics - math problemsStudy plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.
Number of problems found: 2141
- Similar triangles
Triangle A'B'C 'is similar to triangle ABC, whose sides are 5 cm, 8 cm, and 7 cm long. What is the length of the sides of the triangle A'B'C' if its circumference is 80 cm?
- 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].
- The triangles
The triangles ABC and A'B'C 'are similar with a similarity coefficient of 2. The angles of the triangle ABC are alpha = 35°, beta = 48°. Determine the magnitudes of all angles of triangle A'B'C '.
- Edge of prism
The regular quadrilateral prism has a surface of 250 dm2, its shell has a content of 200 dm2. Calculate its leading edge.
- Calculate 6
Calculate the distance of a point A[0, 2] from a line passing through points B[9, 5] and C[1, -1].
- Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side?
- Powerplant chimney
From the building window at the height of 7.5 m, we can see the top of the factory chimney at an altitude angle of 76° 30 ′. We can see the chimney base from the same place at a depth angle of 5° 50 ′. How tall is the chimney?
- Similar triangles
In the triangle DEF is DE = 21cm, EF = 14.7cm, DF = 28cm. The triangle D´E´F´ is similar to the triangle DEF. Calculate the lengths of the sides of the triangle D´E´F´ if the similarity coefficient is one-seventh.
- Cylinder container
The cylindrical container with a diameter of 1.8 m contains 2,000 liters of water. How high does the water reach?
- Similarity coefficient
In the triangle TMA the length of the sides is t = 5cm, m = 3.5cm, a = 6.2cm. Another similar triangle has side lengths of 6.65 cm, 11.78 cm, 9.5 cm. Determine the similarity coefficient of these triangles and assign similar sides to each other.
- Quadrilateral pyramid
Calculate the volume of a quadrilateral pyramid, the base of which has the shape of a rectangle with dimensions a = 6cm, b = 4cm and height v = 11cm
- Chord of triangle
If the whole chord of the triangle is 14.4 cm long, how do you calculate the shorter and longer part?
- The trench
Calculate how many cubic meters of soil needs to be removed from the excavation in the shape of an isosceles trapezoid, the top width is 3 meters, the lower width is 1.8 m, the depth of the excavation is 1 m, and the length is 20 m.
- Lamps on playground
The playground has the shape of a rectangle 36 x 50m. After how many meters will he place the lamps on his lighting, if the distances between them are to be the same on both sides if the builders want to use the smallest possible number of lamps?
- Largest wall
Find the content of the largest wall of a prism with a rectangle base with a height of 4 dm, side c = 5 cm, and side b = 6 cm.
Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
- Quadrilateral prism
Calculate the surface of a quadrilateral prism according to the input: Area of the diamond base S1 = 2.8 m2, length of the base edge a = 14 dm, height of the prism 1,500 mm.
- Alcohol from potatoes
In the distillery, 10 hl of alcohol can make from 8 t of potatoes. The rectangular field with dimensions of 600 m and 200 m had a yield of 20 t of potatoes per hectare. How many square meters of area are potatoes grown to obtain one liter of alcohol?
- Trip with compass
During the trip, Peter went 5 km straight north from the cottage, then 12 km west and finally returned straight to the cottage. How many kilometers did Peter cover during the whole trip?
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