# Pythagorean theorem - examples - page 4

- Diagonal

Determine the dimensions of the cuboid, if diagonal long 31 dm has angle with one edge 61° and with other edge 52°. - Infinity

In a square with side 9 is inscribed circle, in circle is inscribed next square, again circle and so on to infinity. Calculate the sum of area of all these squares. - Ladder

Ladder 8 m long is leaning against the wall. It foot is 1 m away from the wall. In which height ladder touch the wall? - R Trapezium

Rectangular trapezium has bases 12 and 5 and area 84 cm^{2}. What is its perimeter? - Triangle

Can be rectangular triangle equilateral? - Octagon

We have a square with side 84 cm. We cut the corners to make his octagon. What will be the side of the octagon? - Pyramid roof

1/3 of area of the roof shaped regular tetrahedral pyramid with base edge 9 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered? - Cube - angles

Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base. - Cap

Jesters hat is shaped a rotating cone. Calculate how much paper is needed to the cap 60 cm high when head circumference is 52 cm. - Sphere slices

Calculate volume and surface of a sphere, if the radii of parallel cuts r_{1}=31 cm, r_{2}=92 cm and its distance v=25 cm. - Rhombus

Find the length of the other diagonal and area of rhombus. The perimeter of a rhombus is 40 cm and one of the diagonals is of length 10 cm. - Tetrahedral pyramid

Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm and the length of the edges of the base is 6 cm. - Climb

On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went? - ISO triangle

Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm. - Triangular prism

Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 39 degrees, |AB| = 3 cm. Calculate the volume of the prism. - Recursion squares

In the square ABCD is inscribed a square so that its vertices lie at the centers of the sides of the square ABCD.The procedure of inscribing square is repeated this way. Side length of square ABCD is a = 22 cm. Calculate: a) the sum of perimeters of all - Diagonals of the rhombus

Calculate height of rhombus whose diagonals are 12 cm and 19 cm. - Rhombus 2

Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long. - Leg and height

Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m. - Similarity coefficient

The ratio of similarity of two equilateral triangles is 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of the larger triangle.

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Pythagorean theorem is the base for the right triangle calculator.