Square + right triangle - math problems

Number of problems found: 73

Digging a pit
The pit has the shape of a regular quadrilateral truncated pyramid. The edges of the bases are 14m and 10m long. The sidewalls form an angle of 135° with a smaller base. Determine how many m³ of soil were excavated when digging the pit?
Truncated pyramid
The concrete pedestal in the shape of a regular quadrilateral truncated pyramid has a height of 12 cm, the pedestal edges have lengths of 2.4 and 1.6 dm. Calculate the surface of the base.
Quadrilateral pyramid
In a regular quadrilateral pyramid, the height is 6.5 cm and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body. Round calculations to 1 decimal place.
Flakes
A circle was described on the square, and a semicircle above each side of the square was described. This created 4 "flakes". Which is bigger: the content of the central square or the content of four chips?
Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
Find the
Find the surface area of a regular quadrilateral pyramid which has a volume of 24 dm³ and a height of 45 cm.
Quadrilateral pyramid
The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base
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
Height of pyramid
The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height?
Quadrilateral prism
The height of a regular quadrilateral prism is v = 10 cm, the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the volume of the prism.
Distance of points
A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S.
Squares above sides
Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm². 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?
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°.
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.
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?
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.
Body diagonal
Calculate the length of the body diagonal of the 6cm cube.
Annular area
The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.
Same area
There is a given triangle. Construct a square of the same area.

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