Planimetrics - math word problems

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.

Triangle ABC
Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle a) rectangular b) acute-angled?
Right triangles
How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget to the triangle inequality).
Drainage channel
The cross section of the drainage channel is an isosceles trapezoid whose bases have a length of 1.80 m, 0.90 m and arm has length 0.60 meters. Calculate the depth of the channel.
Fence
Square garden has an area of 537 m². How many meters netting is necessary to fence the garden?
Katy MO
Kate draw triangle ABC. Middle of AB have mark as X and the center of the side AC as Y. On the side BC wants to find the point Z such that the content area of a 4gon AXZY was greatest. What part of the triangle ABC can maximally occupy 4-gon AXZY?
Diagonals in diamond
In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
Carpet
What is the price of square carpet side length 3.25 m if one meter square cost 230 CZK?
Trapezoid
Area of trapezoid is 135 cm². Sides a, c and height h are in a ratio 6:4:3. How long are a,c and h? Make calculation...
Air pressure
The meteorological station measured the air pressure of 1060 hPa (hectopascals). In addition to measuring instruments, there is a residential house that has a flat roof with dimensions of 10 m and 28 m. What pressure force in MN (meganewtons) force the a
Diameter
The diameter of a circular plot is 14 dm. Find the circumference and area.
Forces
Determine the resultant of two perpendicular forces F₁ = 560 N and second force of 25% smaller.
Cableway
Cableway has a length of 1800 m. The horizontal distance between the upper and lower cable car station is 1600 m. Calculate how much meters altitude is higher upper station than the base station.
Rhombus IV
Calculate the length of the diagonals of the rhombus, whose lengths are in the ratio 1: 2 and a rhombus side is 35 cm.
Pentagon
Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
Flywheel
Flywheel turns 450 rev/min (RPM). Determine the magnitude of the normal acceleration of the flywheel point which are at a distance of 10 cm from the rotation axis.
Broken tree
The tree was 35 meters high. The tree broke at a height of 10 m above the ground. Top but does not fall off it refuted on the ground. How far from the base of the tree lay its peak?
Ferris wheel
Ferris wheel reaches to 22 m tall and moves at the speed of 0.5m/s. During one drive wheel rotates three times. What is the total drive time?
Journey
Charles and Eva stands in front of his house, Charles went to school south at speed 5.4 km/h, Eva went to the store on a bicycle eastwards at speed 21.6 km/h. How far apart they are after 10 minutes?
Dusan
a) Dusan break two same window, which has triangular shape with a length of 0.8 m and corresponding height 9.5 dm. Find how many dm² of glass he needs to buy for glazing of these windows. b) Since the money to fix Dusan has not, must go to the paint jo
Alfa, beta, gama
In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC.

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