# Examples of area of plane shapes - page 25

1. KLMN trapezoid The KLMN trapezoid has bases KL 40cm and MN 16cm. On the KL base is point P. The segment NP divides the trapezoid into units with the same area. What is the distance of point P from point K?
2. Rectangle diagonal The rectangle, one side of which is 5 cm long, is divided by a 13 cm diagonal into two triangles. Calculate the area of one of these triangles in cm2.
3. 3d printer 3D printing ABS filament with diameter 1.75 mm has density 1.04 g/cm3. Find the length of m = 5 kg spool filament. (how to calculate length)
4. Diagonals of pentagon Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
5. Square Calculate the area of the square shape of the isosceles triangle with the arms 50m and the base 60m. How many tiles are used to pave the square if the area of one tile is 25 dm2?
6. Rectangle - area, perimeter The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.
7. Waste How many percents are waste from a circular plate with a radius of 1 m from which we cut a square with the highest area?
8. Volcano The crater of a volcano is approximately in the shape of a cone of a base 3.1416 sq. Mi. The crater's depth is 1500 ft. How many cubic yards of earth would be required to fill this cavity?
9. Three segments 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?
10. Pool tiles The pool is 25m long, 10m wide and 160cm deep. How many m2 of tiles will be needed on the walls and the pool? How many pieces of tile are needed when 1 tile has a square shape with a 20cm side? How much does it cost when 1m2 of tiles costs 258 Kc?
11. Circle simple Circumference of a circle is 6.28. What is the area of the circle?
12. Perimeter of square The square has a circumference 17cm. What is its area?
13. One hectare How many square meters are one hectare?
14. Cube cut The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '.
15. Hexagon ABCDEF In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
16. Tetrahedral pyramid Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m.
17. Cutting square From a square with a side of 30 cm, we cut the circle with the highest possible diameter. How many percents of the square content is this circle?
18. Sss triangle Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
19. Square metal sheet Four squares of 300 mm side were cut out from a square sheet metal plate with a side of 0,7 m. Express the fraction and the percentage of waste from the square metal sheet.
20. Isosceles trapezoid The old father decided to change the top plate of an isosceles-like trapezoid with the basic dimensions of 120 cm and 60 cm, and the shoulder is 50 centimeters long. How much does it pay for a new plate and a square meter worth 17 euros?

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