# Area of shape + Pythagorean theorem - math problems

- Triangular prism

The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism. - Triangular prism,

The regular triangular prism, whose edges are identical, has a surface of 2514 cm ^ 2 (square). Find the volume of this body in cm^{3}(l). - Free space in the garden

The grandfather's free space in the garden was in the shape of a rectangular triangle with 5 meters and 12 meters in length. He decided to divide it into two parts and the height of the hypotenuse. For the smaller part creates a rock garden, for the large - Hexagonal pyramid

Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm. - The quadrilateral pyramid

The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area. - Squares above sides

Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm^{2}. The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc - Tetrahedral pyramid

Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´. - Eq triangle minus arcs

In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts - Hexagon

Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm. - The trapezium

The trapezium is formed by cutting the top of the right-angled isosceles triangle. The base of the trapezium is 10 cm and the top is 5 cm. Find the area of trapezium. - The plaster cast

The plaster cast has the shape of a regular quadrilateral pyramid. The cover consists of four equilateral triangles with a 5 m side. Calculate its volume and surface area. - The tractor

The tractor sows an average of 1.5 ha per hour. In how many hours does it sows a rectangular trapezoid field with the bases of 635m and 554m and a longer arm 207m? - Company logo

The company logo consists of a blue circle with a radius of 4 cm, which is an inscribed white square. What is the area of the blue part of the logo? - Area of a rectangle

Calculate the area of a rectangle with a diagonal of u = 12.5cm and a width of b = 3.5cm. Use the Pythagorean theorem. - 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}. - Three altitudes

A triangle with altitudes 4; 5 and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle. - Isosceles triangle 9

Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm and altitude is 24cm. Find the area of the isosceles triangle - Annular area

The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area. - Ratio of sides

Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7. - Pyramid height

Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.

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Pythagorean theorem is the base for the right triangle calculator.