# Area - 7th grade (12y) - examples

1. Iceberg
What is the surface area of 50 cm iceberg (in the shape of a cuboid) that can carry a man with luggage with a total weight of 120 kg?
2. Garden
Area of a 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. Square
Points A[-5,-6] and B[7,-1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
4. Right triangle Alef
The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
5. Circle arc
Circle segment has a circumference of 135.26 dm and 2096.58 dm2 area. Calculate the radius of the circle and size of central angle.
6. Gutter
How much metal is needed for production 46 pieces of gutter pipes with the diameter 12 cm and length of 4 m? The plate bends add 2% of the material.
7. Present
Gift box has rectangular shape with dimensions of 8×8×3 cm. Miloslav wants to cover with square paper with sides of 18 cm. How much paper left him?
8. Cone
Circular cone of height 15 cm and volume 5699 cm3 is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
9. Expansion
If one side of the rectangle is larger 4-times and second 2-times, what percentage increases the area of rectangle?
10. Cu thief
The thief stole 122 meters copper wire with cross-section area of 95 mm2. Calculate how much money gets in the scrap redemption, if redeemed copper for 5.5 eur/kg? The density of copper is 8.96 t/m3.
11. Cap
Jesters hat is shaped a rotating cone. Calculate how much paper is needed to the cap 60 cm high when head circumference is 52 cm.
12. Right isosceles
Calculate area of the isosceles right triangle which perimeter is 41 cm.
13. Copper sheet
The copper plate has a length of 1 m, width 94 cm and weighs 9 kg. What is the plate thickness, if 1 m3 weighs 8715 kg?
14. Canopy
Mr Peter has metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 3.3 m2?
15. 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?
16. Rotating cone II
Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
17. Magnification of the square
If we increase the square side, increase the content of the 80 %. About what percentage was increased his sides?
18. 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.
19. Equilateral triangle
Calculate the side of an equilateral triangle, if its area is 892 mm2.
20. Leveling
Calculate how many 25 kg bags of leveling concrete must be purchased if we leveling room 15 m2 to the "height" 6 mm if consumtion is 1.5 kg per square meter and millimeter thickness.

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