# Pythagorean theorem - math word problems

1. Rectangular trapezium Calculate the perimeter of a rectangular trapezium when its content area is 576 cm2 and sice a (base) is 30 cm, height 24 cm.
2. Cone container Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
3. Lamp cone Calculate the surface of a lamp shade shaped of a rotary truncated cone with base diameter 32 cm and 12 cm and height 24 cm.
4. Perimeter of circle Calculate the circumference of described circle to the triangle with sides 9,12,15 cm.
5. Triangular prism Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume.
6. Triangle KLB It is given equilateral triangle ABC. From point L which is the midpoint of the side BC of the triangle it is drwn perpendicular to the side AB. Intersection of perpendicular and the side AB is point K. How many % of the area of the triangle ABC is area
7. Rectangle The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle.
8. Prism Find the volume and surface area of prism with base of an equilateral triangle with side 7 dm long and the body height of 1.5 m.
9. Hexa prism Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm.
10. Vertical prism The base of vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism
11. Two balls Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
12. Diagonals in diamons/rhombus Rhombus ABCD has side length AB = 4 cm and a length of one diagonal of 6.4 cm. Calculate the length of the other diagonal.
13. Float boya A 0.5 meter spherical float is used as a location mark for a fishing boat anchor. It floats in salt water. Find the depth to which the float sinks if the material of which the float is made weighs 8 kilograms per cubic meter and salt water weighs 1027 kg/ A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter.
15. The ditch Ditch with cross section of an isosceles trapezoid with bases 2m 6m are deep 1.5m. How long is the slope of the ditch?
16. 6 regular polygon It is given 6 side regular polygon whose side is 5 cm. Calculate its content area. Compare how many more cm2 (square centimeters) has a circle in which is inscribed the 6-gon.
17. Chors centers The circle with a diameter 17 cm, upper chord /CD/ = 10.2 cm and bottom chord /EF/ = 7.5 cm. The midpoints of the chords H, G is that /EH/ = 1/2 /EF/ and /CG/ = 1/2 /CD/. Determine the distance between the G and H, if CD II EF (parallel).
18. Inscribed circle Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1].
19. Hexagon area The center of the regular hexagon is 21 cm away from its side. Calculate the hexagon side and its area.
20. Tent Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m.

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...

Pythagorean theorem is the base for the right triangle calculator.