Pythagorean theorem - math word problems

Medians in RT
The rectangular triangle ABC has a length of 10 cm and 24 cm. Points P, Q, R are the centers of the sides of this triangle. The perimeter of the PQR triangle is:
Triangular prism - regular
The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism.
Kostka
Kostka je vepsána do koule o poloměru r = 6 cm. Kolik procent tvoří objem kostky z objemu koule?
Horses playground
The fence for the horses has the shape of a rectangular trapezoid with an area of 400 m², the base lengths should be 31 m and 19 m. How many meters of boards will they need to fence it if the boards are stacked in 5 rows?
Compute 4
Compute the exact value of the area of the triangle with sides 14 mi, 12 mi, and 12 mi long.
Triangular prism
The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.
Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
Chord BC
A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates: [- 14; 0]?
Right angle
If a, b and c are two sides of a triangle ABC, a right angle in A, find the value on each missing side. If b=10, c=6
Angle of the body diagonals
Using vector dot product calculate the angle of the body diagonals of the cube.
Five-gon
Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.
What percentage
What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km
Triangular prism,
The regular triangular prism, whose edges are identical, has a surface of 2514 cm ^ 2 (square). Find the volume of this body in cm³ (l).
Three faces of a cuboid
The diagonal of three faces of a cuboid are 13,√281 and 20 units. Then the total surface area of the cuboid is.
Free space in the garden
The grandfather's free space in the garden was in the shape of a rectangular triangle with 5 meters and 12 meters in length. He decided to divide it into two parts and the height of the hypotenuse. For the smaller part creates a rock garden, for the large
Top of the tower
The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joint
Suppose
Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?
A cell tower
A cell tower is located at coordinates (-5, -7) and has a circular range of 12 units. If Mr. XYZ is located at coordinates (4,5), will he be able to get a signal?
Storm and roof
The roof on the building is a cone with a height of 3 meters and a radius equal to half the height of the roof. How many m² of roof need to be repaired if 20% were damaged in a storm?
Hexagonal pyramid
Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm.