Pythagorean theorem - high school - practice problems - page 10 of 30
Number of problems found: 600
- Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the circle’s radius that passes through vertices B, C, and the center of the side AD. - The tent
The tent has the shape of a regular square pyramid. The edge of the base is 3 m long, and the tent's height is 2 m. Calculate how much cover (without a floor) is used to make a tent. - Cross-section 23491
The cross-section of the railway embankment is an isosceles trapezoid, the bases of which are in a ratio of 5:3. The arms have a 5 m embankment height v = 4.8 m. Calculate the section area S. - Difference 23481
The distance as the crow flies between Dolní and Horní Ves is 3 km, and the steady climb is 5%. What is the height difference between Horní and Dolní Ves rounded to the nearest meter?
- Circumscribed 22713
Calculate the circumference and the area of a regular ten-angle polygon if the radius of the circumscribed circle r = 20 cm. - Cone roof
How many m² of roofing is needed to cover a cone-shaped roof with a diameter of 10 m and a height of 4 m? Add an extra 4% to the overlays. - Spherical cap
The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut. - Quadrilateral 21523
Calculate the surface area and volume of a regular quadrilateral pyramid if the edge of the lower base is 18 cm and the edge of the upper base is 15 cm. The wall height is 9 cm. - Embankment
The railway embankment 300 m long has a cross-section of an isosceles trapezoid with bases of 14 m and 8 m. The trapezoidal arms are 5 m long. Calculate how much m³ of soil is in the embankment.
- Difference of legs
In a right triangle, the hypotenuse length is 65 m, and the difference between legs is 23 m. Calculate the perimeter of this triangle. - RT triangle and height
Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm. - An equilateral
An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle? - Triangular prism - regular
The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism. - Cube in sphere
The cube is inscribed in a sphere with a radius r = 6 cm. What percentage is the cube's volume from the ball's volume?
- Horses playground
The fence for the horses has the shape of a rectangular trapezoid with an area of 400 m². The base lengths should be 31 m and 19 m. How many meters of boards will they need to fence if they are stacked in 5 rows? - Compute 4
Compute the exact value of the triangle area with sides 14 mi, 12 mi, and 12 mi long. - Triangular prism
The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism. - Quadrilateral 19413
Calculate the surface area of a regular quadrilateral pyramid given: a= 3.2 cm h= 19 cm Method: 1) calculation of the height of the side wall 2) content of the base 3) shell contents 4) the surface of a regular quadrilateral pyramid - Surface 19383 cone
The volume of a cone with a radius of 6 cm is 301.44 cm cubic. What is its surface?
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