Pythagorean theorem - math word problems - page 55 of 68
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: 1342
- Quadrilateral 8120
Include the side edge length of a regular quadrilateral pyramid if the pyramid height is 4 cm and the base area is 16 cm². - Calculate 6566
Calculate the surface area and volume of a regular hexagonal pyramid whose base edge is 10 cm long and the side edge is 26 cm long. - Calculate 6331
The regular hexagonal pyramid has a base edge of 20 cm and a side edge of 40 cm. Calculate the height and surface of the pyramid - Quadrilateral 5112
The body diagonal of a regular quadrilateral prism forms an angle of 60 ° with the base. The edge of the base is 20 cm long. Calculate the volume of the body.
- Axial cut
The cone surface is 388.84 cm2, and the axial cut is an equilateral triangle. Find the cone volume. - How to
How to find a total surface of a rectangular pyramid if each face is 8 dm high and the base is 10 dm by 6 dm? - Triangular pyramid
Calculate the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height v = 20cm. - Volume of the cone
Calculate the cone's volume if its base area is 78.5 cm² and the shell area is 219.8 cm². - Cone - from volume surface area
The volume of the rotating cone is 1,018.87 dm3, and its height is 120 cm. What is the surface area of the cone?
- 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. - 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. - 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? - Prism 4 sides
The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters - Square pyramid
Calculate the pyramid's volume with the side 5 cm long and with a square base, and the side base has an angle of 60 degrees.
- Nice prism
Calculate the cuboid's surface if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm. - Tetrahedral pyramid
It is given a regular tetrahedral pyramid with a base edge of 6 cm and a height of pyramid 10 cm. Calculate the length of its side edges. - Cone and the ratio
The rotational cone has a height of 43 cm, and the ratio of the base surface to the lateral surface is 5: 7. Calculate the surface of the base and the lateral surface. - Circumference of edges
The hexagon pyramid has a circumference of 120 cm, and the length of the side edge is 25 cm. Calculate its volume. - Quadrilateral 39333
The tent with the floor has the shape of a regular quadrilateral pyramid with a base edge a = 2.4 m and a height of 1.8 m. How much canvas is needed for the tent?
Do you have homework that you need help solving? Ask a question, and we will try to solve it.