# Examples of area of plane shapes

1. Right-angled triangle
Determine the content of a right triangle whose side lengths form successive members of an arithmetic progression and the radius of the circle described by the triangle is 5 cm.
2. Garden
The rectangular garden has dimensions of 27 m and 30 m. Peter and Katka split it in a ratio of 4:5. How many square meters did Katkin measure part of the garden?
3. Two annuluses
The area of the annular circle formed by two circles with a common center is 100 cm2. The radius of the outer circle is equal to twice the radius of the inner circle. Determine the outside circle radius in centimeters.
4. Diagonal
he rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has area 15cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal.
5. Garden fence
The garden has the shape of a rectangular triangle with an area of 96 square meters and a 16 m long one leg. How many meters of the fence need to be fenced?
6. Area of rectangle
Calculate the area of rectangle in square meters whose sides have dimensions a = 80dm and b = 160dm.
Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =?
8. Circle simple
Circumference of a circle is 6.28. What is the area of the circle?
9. Rectangle 39
Find the perimeter and area of the rectangular with vertices (-1, 4), (0,4), (0, -1), and (-4, 4)
10. 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?
11. Inscribed circle
The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.
12. 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.
13. 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
14. 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.
15. Square area
Complete the table and then draw each square. Provide exact lengths. Describe any problems you have. Side Length Area
16. Cube wall
The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube.
17. 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.
18. 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.
19. 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.
20. 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?

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