# Pythagorean theorem - problems - page 18

- Square

Calculate the side of a square with a diagonal measurement 10 cm. - Two diagonals

The rhombus has a side length 12 cm and length of one diagonal 21 cm. What is the length of the second diagonal? - Four sided prism

Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane. - Trio 2

Decide whether trio of numbers is the side of a right triangle: 26,24,10. - Add vector

Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ. - 30-gon

At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area. - Cableway

Cableway has a length of 1800 m. The horizontal distance between the upper and lower cable car station is 1600 m. Calculate how much meters altitude is higher upper station than the base station. - Four ropes

TV transmitter is anchored at a height of 44 meters by four ropes. Each rope is attached at a distance of 55 meters from the heel of the TV transmitter. Calculate how many meters of rope were used in the construction of the transmitter. At each attachment. - Is right triangle

Decide if the triangle XYZ is rectangular: x = 4 m, y = 6 m, z = 4 m - Isosceles trapezoid

Calculate the circumference and the contents of the isosceles trapezoid if you know the size of the bases is 8 and 12 cm and the size of the arms is 5 cm. - Chord circle

The circle to the (S, r = 8 cm) are different points A, B connected segment /AB/ = 12 cm. AB mark the middle of S'. Calculate |SS'|. Make the sketch. - Church roof 2

The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m^{2}of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste? - Land - isosceles trapezoid

Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m. - Hypotenuse

Calculate the length of the hypotenuse of a right triangle with a cathetuses 71 cm and 49 cm long. - Cuboid easy

The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid. - Body diagonal

Find the cube surface if its body diagonal has a size of 6 cm. - Diagonals of diamond

Find the area and circumference of the diamond ABCD with 15m and 11m diagonals. - Axial cut

The cone surface is 388.84 cm^{2,}the axial cut is an equilateral triangle. Find the cone volume. - Stadium

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. - Circle's chords

In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle.

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Pythagorean theorem is the base for the right triangle calculator.