Pythagorean theorem - math word problems - page 61 of 67
The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as:c2 = a2 + b2
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
A common proof of the Pythagorean Theorem is called the "area proof". To prove the theorem using this method, we can create a square with side length c and two smaller squares with side lengths a and b, as shown in the figure. We can then place the smaller squares next to each other to form a rectangle with area a x b. We can then see that the area of the square with side length c is equal to the sum of the areas of the smaller squares, which is equal to the area of the rectangle. This demonstrates that c2 = a2 + b2, as stated in the theorem.
Another proof is Euclidean proof which is based on the Euclidean geometry and construction of a line segment that is c and perpendicular to the line segment of a and b.
Number of problems found: 1340
- The plaster cast
The plaster cast has the shape of a regular quadrilateral pyramid. The cover consists of four equilateral triangles with a 5 m side. Calculate its volume and surface area. - Distance of lines
Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm - Cuboid easy
The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid. - Pyramid 4sides
Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the pyramid's height is 7 cm.
- Concrete block
Determine the volume of the concrete block whose one edge of the base has a length of 3 meters, body diagonal is 13 meters, and height is 12 meters. - Spherical cap
From the sphere with a radius of 11 was a truncated spherical cap. Its height is 6. What part of the volume is a spherical cap from the whole sphere? - Axial section
The axial section of the cone is an equilateral triangle with an area 208 m². Calculate the volume of the cone. - Quadrilateral 83307
The diagonal of section DBFH of the regular quadrilateral prism ABCDEFGH inscribes a circle with a diameter of 8 cm. What is the volume of the prism? - Quadrilateral 83272
Calculate the surface area and volume of a regular quadrilateral pyramid whose base edge is 5 cm long and whose height is 10 cm.
- Calculate 82073
Calculate a cone's volume and surface area with base diameter d = 22 cm and body height v = 40 cm. - Millimeter 81160
Calculate the length of the side of the cone; they rounded the result to tenths of a millimeter. If you know: radius 24 mm and height 46 mm - Quadrilateral 69834
What is the volume of a regular quadrilateral pyramid? The pyramid height is 30 cm, and the wall height is 50 cm. - Calculate 65354
Calculate the surface of a spherical paragraph with a height of 6 cm and a radius of 15 cm - Surface 64744
The cone is 12 cm high, and the radius of the figure is 9 cm. Find out its surface.
- Regular 4-sided pyramid
Find the area (surface area) of a regular 4-sided pyramid if its height is 20 m and the wall height is 23 m. - Calculate 36263
Calculate the surface area and volume of a regular 4-sided pyramid with a base edge of a = 12 cm and a height of v = 5 cm - Quadrilateral 32193
In a regular quadrilateral pyramid, the base edge a = 6cm, the side edge b = 10cm. Calculate the height of the pyramid. - Regular hexagonal prism
Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long. - Quadrilateral 14103
Calculate the volume of a regular quadrilateral pyramid whose wall height is w = 12cm.
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