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

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

One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus. - Rectangular trapezoid

The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid. - Rectangle

The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides. - The rope

A 68 centimetre long rope is used to make a rhombus on the ground. The distance between a pair of opposite side corners is 16 centimetres what is the distance between the other two corners? - Pentagon

Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 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. - Cube diagonal

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

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

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