Planimetrics - practice for 12 year olds - page 48 of 49
Number of problems found: 961
- The land
The land in the shape of a square has 9 ha. How big a side will the land have at a scale of 1:5000? - Swimming 78124
A 16 m square swimming pool has an area of 1 m² on the city plan. What is the scale of the city plan? - Instructions: 56651
Divide the line segment AB into three equal parts. Instructions: Construct an equilateral triangle ABC and find its center (e.g., the described circles). - Outside tangents
Calculate the length of the line segment S1S2 if the circles k1 (S1, 8cm) and k2 (S2,4cm) touch the outside.
- Square 80371
Draw a square EFIJ if EI is equal to 7cm. - Triangle-shaped 30011
Determine the map's scale if the 1.6 km, 2.4 km, and 2.7 km triangle-shaped forests are drawn on the map as a triangle with sides of 32 mm, 48 mm, and 54 mm. - MO Z8–I–6 2018
The KLMN trapezium, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line. - Triangle 28611
The land has a triangle shape with sides of 300m, 200m, and 245m. Draw it on a scale of 1:5 000. - Components 2565
The component is a regular decagon with a side of 2 cm. Its material weight of 1 m² of sheet metal is 24 kg. What is the weight of 200 components?
- Construct 13581
The vertices of the triangle ABC lie on the circle k. The circle k is divided into three parts in a ratio of 1:2:3. Construct this triangle. - Observation 76644
From the smaller observation tower, we see the top of the larger tower at an elevation angle of 23°, and the difference in their heights is 12 m. How far apart are the observation towers? - Difference 81888
The ropeway climbs at an angle of 22°30'. Calculate its length if the height difference between the lower and upper station is 560m. Sketch a picture - Parallelogram
Calculate area of the parallelogram ABCD as shown if |AB| = 13 cm, |BC| = 99 cm and angle BAD = 100° - Hypotenuse 65744
Construct a right triangle ABC with the hypotenuse AB: a) | AB | = 72 mm, | BC | = 51 mm b) | AB | = 58 mm, | AC | = 42 mm
- Divide an isosceles triangle
How to divide an isosceles triangle into two parts with equal areas perpendicular to the axis of symmetry (into a trapezoid and a triangle)? - Kites
Boys run kites on a cable of 68 meters long. What is the kite altitude if the angle from the horizontal plane is 72°? - Diagonals
The rhombus has two diagonals, e=14 dm, and f=11 dm. Calculate the side angle and height of the rhombus. - Circular 82418
A circular segment has an area of 6.04 cm², the central omega angle is 15 degrees, what is the radius? - Maximum area of rhombus
Calculate the interior angles at which the equilateral rhombus has a maximum area.
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