# Ratio + area of shape - examples

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 makes possible to calculate the fourth - unknown member.

1. Area of rectangle
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?
2. Garden
Area of square garden is 6/4 of triangle garden with sides 56 m, 35 m and 35 m. How many meters of fencing need to fence a square garden?
3. Scale
Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 8.25 cm2. What scale is the city plan?
4. Circles
The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.
5. Two squares
Two squares whose sides are in the ratio 5:2 have sum of its perimeters 73 cm. Calculate the sum of area this two squares.
6. Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees.
7. Rectangle - sides ratio
Calculate area of rectangle whose sides are in ratio 3:13 and perimeter is 673.
8. Expansion
If one side of the rectangle is larger 4-times and second 2-times, what percentage increases the area of rectangle?
9. Floor
The floor area of ​​the room is 31 m2 and has a width of 4.3 m. How many centimeters of circumference measured floor on the map at the scale 1:75?
10. Pizza
Pizza with a diameter 50 cm have weight 559 g. What diameter will have a pizza weighing 855 g if it is make from the same cloth (same thickness....) and same decorated?
11. ISO triangle
Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.
12. Axial section
Axial section of the cylinder has a diagonal 31 cm long and we know that the area of the side and the area of base is in ratio 3:2. Calculate the height and radius of the cylinder base.
13. Plan of the village
Plan of the municipality in 1:1000 scale has plotted garden with dimensions 25 mm and 28 mm. Determine the area of gardens in ares in reality.
14. Glass
At the glass shop we have to cut 8 sheets of glass. Each was shaped a square with sides of 18 cm. We paid 44 CZK. How much is a 1 m2 of glass?
15. MO - triangles
On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB se
16. Trapezoid - diagonal
Trapezoid has a length of diagonal AC corssed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm2. What is the area of the trapezoid?
17. Cone and the ratio
Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
18. Axial section
Axial section of the cylinder has a diagonal 40 cm. The size of the shell and the base surface are in the ratio 3:2. Calculate the volume and surface area of this cylinder.
19. Similarity n-gon
9-gones ABCDEFGHI and A'B'C'D'E'F'G'H'I' are similar. The area of 9-gon ABCDEFGHI is S1=190 dm2 and the diagonal length GD is 32 dm. Calculate area of the 9-gon A'B'C'D'E'F'G'H'I' if G'D' = 13 dm.
20. Rectangle
The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle.

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