# Area + Pythagorean theorem - math problems

- Base of prism

The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm^{2}. - Garden

Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden? - Right Δ

A right triangle has the length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle. - Axial section

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

Points A[-5,-6] and B[7,-1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD. - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm^{2}. - Cone A2V

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

Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of the LCD monitor with a diagonal size 20 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous tha - R triangle

Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg. - 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? - 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. - 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. - 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. - Right isosceles

Calculate area of the isosceles right triangle which perimeter is 41 cm. - Canopy

Mr Peter has metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 3.3 m^{2}? - Rotating cone II

Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm. - Cone and the ratio

Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface. - Equilateral triangle

Calculate the side of an equilateral triangle, if its area is 892 mm^{2}. - Sphere - parts

Calculate the area of a spherical cap, which is part of an area with base radius ρ = 9 cm and a height v = 3.1 cm. - Above Earth

To what height must a boy be raised above the earth in order to see one-fifth of its surface.

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Pythagorean theorem is the base for the right triangle calculator.