# Pythagorean theorem - math word problems

1. Body diagonal
Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm
2. Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
3. 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.
4. Medians in right triangle
It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides?
5. Faces diagonals
If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.2, y=1.7, z=1.45
6. Wall and body diagonals
Calculate the lengths of the wall and body diagonals of the cuboid with edge dimensions of 0.5 m, 1 m, and 2 m
7. Tetrahedral pyramid
A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area).
8. Two chords
Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
9. Space diagonal
The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube.
10. Distance between 2 points
Find the distance between the points (7, -9), (-1, -9)
11. The tractor
The tractor sows an average of 1.5 ha per hour. In how many hours does it sows a rectangular trapezoid field with the bases of 635m and 554m and a longer arm 207m?
The ladder has a length of 3 m and is leaning against the wall, and its inclination to the wall is 45°. How high does it reach?
13. Company logo
The company logo consists of a blue circle with a radius of 4 cm, which is an inscribed white square. What is the area of the blue part of the logo?
14. Area of a rectangle
Calculate the area of a rectangle with a diagonal of u = 12.5cm and a width of b = 3.5cm. Use the Pythagorean theorem.
15. Right pyramid
A right pyramid on a base 4 cm square has a slant edge of 6 cm. Calculate the volume of the pyramid.
16. Tree trunk
What is the smallest diameter of a tree trunk that we can cut a square-section square with a side length of 20 cm?
17. Base of prism
The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm2.
18. Touch x-axis
Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
19. Three altitudes
A triangle with altitudes 4; 5 and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle.
20. Isosceles triangle 9
Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm and altitude is 24cm. Find the area of the isosceles triangle

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Pythagorean theorem is the base for the right triangle calculator.