# Examples of area of plane shapes

1. Circle simple
Circumference of a circle is 6.28. What is the area of the circle?
2. Rectangle 39
Find the perimeter and area of the rectangular with vertices (-1, 4), (0,4), (0, -1), and (-4, 4)
3. Cylinder horizontally
The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder?
4. Inscribed circle
The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.
5. MO Z9–I–2 - 2017
In the VODY trapezoid, VO is a longer base and the diagonal intersection K divides the VD line in a 3:2 ratio. The area of the KOV triangle is 13.5 cm2. Find the area of the entire trapezoid.
6. MO8-Z8-I-5 2017
Identical rectangles ABCD and EFGH are positioned such that their sides are parallel to the same. The points I, J, K, L, M and N are the intersections of the extended sides, as shown. The area of the BNHM rectangle is 12 cm2, the rectangle MBCK area is 63.
7. Gardens colony
Gardens colony with dimensions of 180 m and 300 m are to be completely divided into the same large squares of the highest area. Calculate how many such squares can be obtained and determine the length of the square side.
8. Square area
Complete the table and then draw each square. Provide exact lengths. Describe any problems you have. Side Length Area
9. Cube wall
The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube.
10. Isosceles triangle
The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at ratio 5:6. Find the triangle area.
11. Cross section
The cross-section ABCD of a swimming pool is a trapezium. Its width AB=14 meters, depth at the shallow end is 1.5 meters, and at the deep end is 8 meters. Find the area of the cross-section.
12. Pipe cross section
The pipe has an outside diameter 1100 mm and the pipe wall is 100 mm thick. Calculate the cross section of this pipe.
13. Bathroom 2
A bathroom is 2.4 meters long and 1.8 meters wide. How many square tiles 1 dm on each side are to be used to cover it?
14. Rhombus sides
find the sides of a rhombus, it area is 550 cm square and altitude is 55cm
15. Isosceles trapezoid
Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
16. Truncated cone 3
The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, determine the height of the tang.
17. Trapezoidal prism
Calculate the surface of the quadrilateral prism ABCDA'B'C'D 'with the trapezoidal base ABCD. The height of the prism is 12 cm; ABCD trapezoidal data: AB base length is 8 cm, CD base length is 3 cm, BC arm length is 4 cm, and AC diagonal length is 7 cm.
18. Trapezoid - RR
Find the area of the right angled trapezoid ABCD with the right angle at the A vertex; a = 3 dm b = 5 dm c = 6 dm d = 4 dm
19. Rectangle 35
Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length.
20. Circle and rectangle
A rectangle with sides of 11.7 cm and 175 mm is described by circle. What is its length? Calculate the content area of the circle described by this circle.

Do you have an interesting mathematical word problem that you can't solve it? Enter it, 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...