Ratio + area of shape - math problems

On solving problems and tasks with proportionally, we recommend hint rule of three. Rule of three (proportionality) help solve examples of direct and inverse proportionality. Three members make possible to calculate the fourth - unknown member.

  1. The circumference
    rectangle The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?
  2. Half of halves
    sequence_geo 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?
  3. Garden exchange
    land The garden has the shape of a rectangular trapezoid, the bases of which have dimensions of 60 m and 30 m and a vertical arm of 40 m. The owner exchanged this garden for a parallelogram, the area of which is 7/9 of the area of a trapezoidal garden. What is
  4. Squares ratio
    squares2 The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of the contents of these squares? (Write the ratio in the basic form). (Perimeter = 4 * a, conte
  5. Two bodies
    cylinders The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Determine the ratio of surfaces of the first and seco
  6. Diagonal intersect
    rrLichobeznik isosceles trapezoid ABCD with length bases | AB | = 6 cm, CD | = 4 cm is divided into 4 triangles by the diagonals intersecting at point S. How much of the area of the trapezoid are ABS and CDS triangles?
  7. Two rectangles 2
    square_2rectangles A square of area 36 cm2 is cut out to make two rectangles. A and B The area of area A to area B is 2 : 1 Find the dimensions of rectangles A and B.
  8. Ratio of volumes
    cylinder If the heights of two cylindrical drums are in the ratio 7:8 and their base radii are in the ratio 4:3. What is the ratio of their volumes?
  9. Ratio of sides
    described_circle2 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.
  10. Area of rectangle
    rectangle_24 How many times will increase the area of the rectangle, if we increase twice the length and at the same time we decrease the width by the half?
  11. In the
    land_6 In the national park, the ratio of the wooded area to grassland is 4: 1. The total area is 385km2. What area is wooded?
  12. Rectangular plot
    rectangular plot The dimensions of a rectangular plot are (x+1)m and (2x-y)m. If the sum of x and y is 3m and the perimeter of the plot is 36m. Find the area of the diagonal of the plot.
  13. Rectangular field
    rectangle_inside_circle_2 A rectangular field has a diagonal of length 169m. If the length and width are in the ratio 12:5. Find the dimensions of the field, the perimeter of the field and the area of the field.
  14. Three segments
    vysek_1 The circle is divided into 3 segments. Segment A occupies 1/4 of the area, segment B occupies 1/3 of the area. What part is occupied by section C? In what proportion are areas A: B: C?
  15. Cube cut
    cut_cube 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.
  16. Rectangular garden
    garden_21 The sides of the rectangular garden are in ratio 1: 2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden.
  17. Square to rectangle
    square_rot_2 What is the ratio of the area of a square of side x to the area of a rectangle of a rectangle of width 2 x and length 3
  18. The perimeter
    hexagon6 The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX?
  19. Scale of plan
    zahrada_4 On the plan of the village in the scale of 1: 1000 a rectangular garden is drawn. Its dimensions on the plan are 25mm and 28mm. Determine the area of the garden in ares.
  20. Enlarged rectangle
    rectangle_10 The rectangle with dimensions of 8 cm and 12 cm is enlarged in a ratio of 5:4. What are the circumference and the area of the enlarged rectangle?

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