Planimetrics - math word 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: 1973
- The Eiffel Tower
The top of the Eiffel Tower is seen from a distance of 600 meters at an angle of 30 degrees. Find the tower height.
- The double ladder
The double ladder has 3 meters long shoulders. What is the height of the upper of the ladder reach if the lower ends are 1.8 meters apart?
- The bridge
Across the circle lakepasses through its center bridge over the lake. At three different locations on the lake shore are three fishermen A, B, C. Which of fishermen see the bridge under the largest angle?
The tile has the shape of a square with a side of 15 cm. What dimensions can a rectangle composed of 90 of these tiles have so that no tile remains?
How long is a ladder that touches on a wall 4 meters high and its lower part is 3 meters away from the wall?
Rectangular floor of living room has a length 5.4 meters and a circumference 17.2 meters. What is its width?
Meadow is a circle with radius r = 19 m. How long must a rope to tie a goat to the pin on the perimeter of the meadow to allow goat eat half of meadow?
6 m long reservoir has a diameter of 2.2 m. What is its surface area in square meters?
- Central angle
What is the length of the arc of a circle with a diameter of 46 cm, which belongs to a central angle of 30°?
- Cylinder container
The cylindrical container with a diameter of 1.8 m contains 2,000 liters of water. How high does the water reach?
- Space diagonal
The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube.
- The angle of view
Determine the angle of view at which the observer sees a rod 16 m long when it is 18 m from one end and 27 m from the other.
- Diagonals of a rhombus
One of the diagonals of a rhombus is twice as the other. If the sum of the lengths of the diagonals is 24, find the area of the rhombus.
- Isosceles triangle
Calculate the area of an isosceles triangle, the base of which measures 16 cm and the arms 10 cm.
Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
- Diamond side
The diagonals of the diamond are 18 cm and 14 cm long. Calculate the length of the diamond side.
- The parallelogram
The parallelogram has one side 2 dm long, which is one-sixth of its circumference. How many cm does the other side of the parallelogram measure?
- Lake or pond
The landlord has a square lake. Trees grow around this lake. The lake wants to enlarge the pond twice and does not want to cut down or flood any tree. How will he do that?
- Quarter of a circle
Calculate the circumference of a quarter circle if its content is S = 314 cm2.
Forest has an area of 36 ha. How much area is occupied by forest on the map at scale 1:500?
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