9th grade (14y) + Pythagorean theorem - examples
- A box
A box is 15 centimeters long, 4 centimeters wide, and 3 centimeters tall what is the diagonal S of the bottom side? What is the length of the body diagnol R?
- A cylinder
A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm?
- Diamond diagonals
Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm.
- Right angled triangle 3
Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees
- A bridge
A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H
- Equilateral triangle
Calculate the area of an equilateral triangle with circumference 72cm.
- Diagonal to area
Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
Area of square garden is 4/5 of triangle garden with sides 24 m, 15 m and 15 m. How many meters of fencing need to fence a square garden?
- Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid.
- Right Δ
Right triangle has length of one leg 51 cm and length of the hypotenuse 85 cm. Calculate the height of the triangle.
- Cube in a sphere
The cube is inscribed in a sphere with volume 5951 cm3. Determine the length of the edges of a cube.
- Axial section
Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
- Circle chord
What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?
- Trigonometric functions
In right triangle is: ? Determine the value of s and c: ? ?
The rectangle is 31 cm long and 28 cm wide. Determine the radius of the circle circumscribing rectangle.
Cuboid with edge a=23 cm and body diagonal u=41 cm has volume V=13248 cm3. Calculate the length of the other edges.
- Triangle SAS
Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°.
- Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=21 and height v=7?
Points A[-9,6] and B[-5,-3] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 24 km/h, the second at average speed 26 km/h. Determine the distance between them after 35 minutes cycling.
Pythagorean theorem is the base for the right triangle calculator.