Pythagorean theorem - practice for 13 year olds - page 14 of 35
Number of problems found: 689
- Wheel gear
A drive wheel of radius two is connected to a drive wheel of radius one by a pulley of length 17. What is the distance between the wheel axles? - Concentric circles and chord
In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius has the concentric circle while touching this chord? - Pendulum
Calculate the pendulum's length 2 cm lower in the lowest position than in the highest position. The circular arc length to be described when moving is 20cm. - Square
Dan's father has a square of 65.25 milligram square of wire with a diagonal. How will the square be big when one mm weighs 7 mg? - A mast
The wind broke a mast 32 meters high so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part, and the ground form a rectangular triangle. At what height was the mast broken? - Right trapezoid
The right trapezoid has bases 3.2 cm and 62 mm long. The shorter leg has a length of 0.25 dm. Calculate the lengths of the diagonals and the second leg. - Again saw
We have a sculpture beam from the tree trunk with a rectangular cross-section with dimensions 91 mm and 87 mm. What is the trunk's smallest diameter? - Road embankment
Road embankment has a cross-section shape of an isosceles trapezoid with bases 5 m and 7 m and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters? - Chord
In a circle with a radius r=60 cm is the chord, 4× longer than its distance from the center. What is the length of the chord? - Crossbars 80697
Calculate the length of the middle crossbars in an isosceles triangle if the length of the arm is 52mm and the base height is 48mm - Difference 80618
A regular hexagon is described and inscribed in a circle. The difference between its areas is 8√3. Find the circle's radius. - Fifteen-spruce 57291
A mighty gale broke the top of the fifteen-spruce spruce, resting it on the ground. The distance of this top from the trunk was 4.6 m below. At what height was the spruce trunk broken? - Calculate 47763
Calculate the area of an isosceles trapezoid ABCD, whose longer base measures 48 cm, the shorter base measures 3/4 of the longest base, and the leg of the trapezoid measures 2/3 of the longer base. The result is rounded to the nearest hundredth. - Circumference 7823
The bases are 9 cm and 5 cm long in a rectangular trapezoid. The length of the shorter arm is 3 cm. Calculate its circumference and area. - Isosceles 5575
The picture shows an isosceles triangle VLK with a center of gravity of T. The base VL measures 16 cm, and the line KK1 measures 18 cm. How long is the VV1 line? - Circumference 5254
Calculate the shorter side and the diagonal of the rectangle if one side is 2 cm longer than the other and its circumference is equal to 70 centimeters. - Diagonals 5113
In the diamond KLMN, the lengths of the diagonals are 10 cm and 6 cm. Determine the angle size that the longer diagonal makes with the side of the diamond. - Equilateral 4301
Triangle ABC is equilateral with a side length of 8 cm. Points D, E, and F are the sides AB, BC, and AC midpoints. Calculate the area of triangle DEF. In what ratio is the area of triangle ABC to the area of triangle DEF? - Calculate 3161
In the isosceles trapezoid ABCD, the arm is 5.2 cm long, the middle bar is 7 cm long, and the height is 4.8 cm. Calculate the lengths of both bases. - Diagonals of rhombus
Find the length of the diagonal AC of the rhombus ABCD if its perimeter P = 112 dm and the second diagonal BD has a length of 36 dm.
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