# Examples of area of plane shapes

1. Rhombus
The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
2. Ratio of sides 2
The ratio of the side lengths of one square to another is 1:2. Find the ratio of the area of the two squares.
3. Glass panel
A rectangular glass panel with dimensions of 72 cm and 96 cm will cut the glazier on the largest square possible. What is the length of the side of each square? How many squares does the glazier cut?
4. Square
Square JKLM has sides of length 24 cm. Point S is the center of LM. Calculate the area of the quadrant JKSM in cm2.
5. 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?
6. Hypotenuse - RT
A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
7. Hexagon ABCDEF
In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
8. Diamond diagonals
Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm.
9. Cube cut
The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '.
10. Divide
Divide area of rectangles with dimensions 32m and 10m by the ratio 7: 9. What area corresponds to a smaller section?
11. Roof cover
Above the pavilion with a square ground plan with a side length of a = 12 m is a pyramid-shaped roof with a height v = 4.5 m. Calculate how much m2 of sheet metal is needed to cover this roof if 5.5% of the sheet we must add for joints and waste.
12. The room
The room has a cuboid shape with dimensions: length 50m and width 60dm and height 300cm. Calculate how much this room will cost paint (floor is not painted) if the window and door area is 15% of the total area and 1m2 cost 15 euro.
13. Equilateral triangle
Calculate the area of an equilateral triangle with circumference 72cm.
14. 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?
15. Diagonal to area
Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
16. Map scale
The rectangular plot has in a scale of 1: 10000 area 3 cm2 on the map. What content does this plot have on a 1:5000 scale map?
17. Coordinate axes
Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y.
18. Trapezoid - intersection of diagonals
In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area.
19. Annual rainfall
The average annual rainfall is 686 mm. How many liters will fall on the 1-hectare field?
20. Rectangle area
The length of a rectangle of x units is increased by 10% and its width of y units is increased by 15%. What is the ratio of the area of the old rectangle to the area if the new rectangle?

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...