# 9th grade (14y) + Pythagorean theorem - examples

Pythagorean theorem is the base for the right triangle calculator.- Isosceles triangle

Calculate area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm. - Proof PT

Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it. - Logs

Trunk diameter is 72 cm. Is it possible to inscribe a square prism with side 54 cm? - Right Δ

Right triangle has length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle. - MO SK/CZ Z9–I–3

John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball. - Diagonal

Calculate the length of the diagonal of the rectangle ABCD with sides a = 7 cm, b = 6 cm. - Railways

Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters. - Square diagonal

Calculate length of the square diagonal if the perimeter is 200 cm. - Cube diagonal

Determine length of the cube diagonal with edge 91 dm. - Square diagonal

Calculate the length of diagonal of the square with side a = 23 cm. - Circle chord

What is the length d of the chord circle of diameter 58 mm, if distance from the center circle is 24 mm? - Acreage

What acreage has a rectangular plot whose diagonal is 34 meters long and one side has a length of 16 meters. ? - Tetrahedral pyramid

What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=23 and height v=8? - Circumscribing

Determine the radius of the circumscribed circle to the right triangle with legs 3 cm and 10 cm. - Garden

Area of square garden is 6/7 of triangle garden with sides 96 m, 60 m and 60 m. How many meters of fencing need to fence a square garden? - Rhombus

Calculate the perimeter and area of rhombus whose diagonals are 15 cm and 27 cm long. - Rhombus

It is given a rhombus of side length a = 11 cm. Touch points of inscribed circle divided his sides into sections a_{1}= 6 cm and a_{2}= 5 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Spherical cap

From the sphere of radius 12 was truncated spherical cap. Its height is 4. What part of the volume is spherical cap from whole sphere? - Prism

The lenght, width and height of a right prism are 18, 14 and 9 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism? - Oil rig

Oil drilling rig is 23 meters height and fix the ropes which ends are 8 meters away from the foot of the tower. How long are these ropes?

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