# Square + right triangle - math problems

- Tetrahedral pyramid 8

Let’s all side edges of the tetrahedral pyramid ABCDV be equally long and its base let’s be a rectangle. Determine its volume if you know the deviations A=40° B=70° of the planes of adjacent sidewalls and the plane of the base and the height h=16 of the p - Quadrilateral prism

Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°. - 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 - Two circles

Two circles with the same radius r = 1 are given. The center of the second circle lies on the circumference of the first. What is the area of a square inscribed in the intersection of given circles? - 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. - Coordinates of square vertices

I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C 'and D'. Thanks Peter. - 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. - 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? - Angle of two lines

There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV. - Annular area

The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area. - Prism 4 sides

The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters - Prism diagonal

The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism? - Cube cut

In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane. - Waste

How many percents are waste from a circular plate with a radius of 1 m from which we cut a square with the highest area? - Quarter circle

What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm? - Bricklayer

How much do we pay for a bricklayer laying a pavement in a square room with a diagonal of 8 m, if 1 sqm with work will cost for CZK 420? - Angle of diagonal

Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume. - Same area

There is a given triangle. Construct a square of the same area. - Roof cover

Above the pavilion with a square ground plan with a side length of a = 12 m is a pyramid-shaped roof with a height v = 4.5 m. Calculate how much m^{2}of sheet metal is needed to cover this roof if 5.5% of the sheet we must add for joints and waste. - Equilateral triangle

A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.

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