Examples of area of plane shapes - page 25

1. Isosceles trapezium Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm.
2. Cube cut 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.
3. Pilot How high is the airplane's pilot to see 0.001 of Earth's surface?
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. 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?
6. 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?
7. 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.
8. 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)
9. 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?
10. 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?
11. 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.
12. 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?
13. 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?
14. 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?
15. Circle simple Circumference of a circle is 6.28. What is the area of the circle?
16. One hectare How many square meters are one hectare?
17. Perimeter of square The square has a circumference 17cm. What is its area?
18. Cube cut The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '.
19. Pyramid height Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.
20. Hexagon ABCDEF In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.

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