Pythagorean theorem - math word problems - last pageThe 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: 1236
- Area of the cone
Calculate the surface area of the cone. You know the base diameter of 25 cm and a height of 40 cm.
- Cube - angles
Calculate the angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and the cube base.
- Calculate 18843
Height 9cm diameter 24cm cone - calculate its volume and surface.
- Calculate 6580
The rotating cone has a height of 20 cm and a radius of 18 cm. Calculate its surface.
- The diameter 4
The cone's diameter is 14ft, and the height is 7 ft. What is the slant height?
- A prism
A prism with an altitude of 15cm has a base in the form of a regular octagon inscribed in a square of 10cmx10cm. Find the volume of the prism.
- The tetrahedron
Calculate a regular tetrahedron's surface area and volume 4.9 cm high, and the base edge has a length of 6 cm.
- Cube cut
The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '.
A 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
- Body diagonal
Find the cube surface if its body diagonal has a size of 6 cm.
- Cube diagonal
Determine the length of the cube diagonal with edge 37 mm.
- Calculate 4694
Calculate the length of the body diagonal in a cube of 15 cm.
- Octahedron in a cube
What largest octahedron can we place inside a cubical box with sides equal to 72?
- Tetrahedral pyramid
Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m.
- Body diagonal
Calculate the length of the body diagonal of the 6cm cube.
- Spherical cap
What is the surface area of a spherical cap, the base diameter 23 m, and height 3 m?
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