# 8th grade (13y) + Pythagorean theorem - examples

- Area of iso-trap

Find the area of an isosceles trapezoid, if the lengths of its bases are 16 cm, and 30 cm, and the diagonals are perpendicular to each other. - A square

A square with length of diagonals 12cm give: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with length of 16 cm. Calculate the length of the other diagonal. - Find the 3

Find the distance and mid-point between A(1,2) and B(5,5). - Garden

Area of square garden is 4/5 of triangle garden with sides 24 m, 15 m and 15 m. How many meters of fencing need to fence a square garden? - Right Δ

Right triangle has length of one leg 51 cm and length of the hypotenuse 85 cm. Calculate the height of the triangle. - Cube in a sphere

The cube is inscribed in a sphere with volume 5951 cm^{3.}Determine the length of the edges of a cube. - Axial section

Axial section of the cone is equilateral triangle with area 208 dm^{2.}Calculate volume of the cone. - Circle chord

What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m? - Rectangle

The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle. - Tetrahedral pyramid

What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=10 and height v=18? - Triangle SAS

Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°. - Is right?

Is triangle with sides 51, 56 and 77 right triangle? - Square

Points A[-9,6] and B[-5,-3] are adjacent vertices of the square ABCD. Calculate area of the square ABCD. - Movement

From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 24 km/h, the second at average speed 26 km/h. Determine the distance between them after 35 minutes cycling. - Gimli Glider

Aircraft Boeing 767 lose both engines at 45000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1870 feet and maintain constant speed 212 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate - Short cut

Imagine that you are going to the friend. That path has a length 270 meters. Then turn left and go another 1810 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field? - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 dm^{2.}Calculate the volume of a cone. - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 254 cm^{2.} - River

From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river. - Cube diagonal

Determine length of the cube diagonal with edge 33 km.

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Pythagorean theorem is the base for the right triangle calculator.