# Area of shape + expression of a variable from formula - examples

1. Concentric circles
There is given a circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area?
2. The sides 2
The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
3. Right Δ
Right triangle has length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
4. Tereza
The cube has area of base 256 mm2. Calculate the edge length, volume and area of its surface.
5. R Trapezium
Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
6. Arc and segment
Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 33 and corresponding angle is ?.
7. 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.
8. Rhombus 2
Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
9. Circle
How big is area of circle if its circumference is 80.6 cm?
10. Right isosceles
Calculate area of the isosceles right triangle which perimeter is 41 cm.
11. Garden
Trapezoid garden has parallel sides 19 m and 24 m. Its area is 193.5 square meters. What is the width of the garden?
12. Right triangle
Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
13. Perimeter and legs
Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
14. 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.
15. Trapezoid
trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area?
16. Cathethus and the inscribed circle
In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.
17. Rectangle diagonals
It is given rectangle with area 24 cm2 a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
18. Equilateral cylinder
Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
19. 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.
20. Vintner
How high can vintner fill keg with crushed red grapes if these grapes occupy a volume of 20 percent? Keg is cylindrical with a diameter of the base 1 m and a volume 9.42 hl. Start from the premise that says that fermentation will fill the keg (the number.

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