Number of problems found: 249
- Half of halves
Half of the square we cut off, then half of the rest, etc. Five cuts we made in this way. What part of the content of the original square is the content of the cut part?
- Two 2D shapes
Decide which shapes have more area: (a) a square of 8cm side; or (b) two rectangles with sides 5cm and 15cm? Write result as 1 or 2 (rectangles)
- Same area
There is a given triangle. Construct a square of the same area.
- Square sides
If the square side increases by 28%, the square circumference increases by 11.2 meters. Find the length of the original square side.
- The playground
The playground has the shape of a square with a side of 64 m. It is fenced on three sides. What is the area of the playground and how long is its fence?
- Extending square garden
Mrs. Petrová's garden had the shape of a square with a side length of 15 m. After its enlargement by 64 m2 (square), it had the shape of a square again. How many meters has the length of each side of the garden been extended?
3750 cm square of wallpaper is needed to glue a cube-shaped box. Can Dad cut out the whole necessary piece of wallpaper as a whole if he has a roll of wallpaper 50 cm wide?
- Edge of prism
The regular quadrilateral prism has a surface of 250 dm2, its shell has a content of 200 dm2. Calculate its leading edge.
- Mrak - cloud
It is given segment AB of length 12 cm, where one side of the square MRAK laid on it. MRAK's side length 2 cm shown. MRAK gradually flips along the line segment AB the point R leaves a paper trail. Draw the whole track of point R until square can do the l
- Rectangular land
On a rectangular land with dimensions of 35 m and 18.5 m is a house with a square floor plan with a side of 14 m. What % of the land is not occupied?
- 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
- Annular area
The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.
From a square of 12 dm perimeter is cut smaller square, whose side is the third side of the square. What is the area of the rest?
On the special playground, there are 81 square sectors, each with a side of 5 m. How many players can fit on the playground if each player needs a 75 m2 area to play?
- 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.
- Truncated cone 6
Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1.
- 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.
- Glass panel
A rectangular glass panel with dimensions of 72 cm and 96 cm will cut the glazier on the largest square possible. What is the length of the side of each square? How many squares does the glazier cut?
- 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?
- 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