# Examples of area of plane shapes

1. Three shapes
1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?
2. Triangular prism
Calculate the volume and surface of the triangular prism ABCDEF with base of a isosceles triangle. Base's height is 16 cm, leg 10 cm, base height vc = 6 cm. The prism height is 9 cm.
3. Diameters of circles
How many percent of the area of a larger circle is a smaller circle if the smaller circle has a diameter 120 mm and a larger one has a diameter 300 mm?
4. Diamond diagonals
Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.
5. Cutting circles
From the square 1 m side we have to cut the circles with a radius of 10 cm. How many discs we cut and how many percent will be waste?
6. Diameter
What is the inside diameter of the cylinder container and if half a liter of water reaches a height 15 cm?
7. Pagans
Elena cut out same circle-shaped pagans and put them on a rectangular sheet so that the neighboring pagans were touching each other and the pagans were touching the walls of the sheet on the edges. Each pagans occupied 28.26 cm2 of the bottom of the sheet.
8. Parallelogram +ľ
| AB | = 76cm, | BC | = 44cm, angle BAD = 30 °. Find the area of the parallelogram.
9. Juice box
The juice box has a volume of 200ml with its base is an isosceles triangle with sides a = 4,5cm and a height of 3,4cm. How tall is the box?
10. Hexagonal prism
The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism!
11. Children pool
The bottom of the children's pool is a regular hexagon with a = 60 cm side. The distance of opposing sides is 104 cm, the height of the pool is 45 cm. A) How many liters of water can fit into the pool? B) The pool is made of a double layer of plastic film
12. Annulus
The radius of the larger circle is 8cm, the radius of smaller is 5cm. Calculate the contents of the annulus.
13. Four circles
1) Calculate the circle radius if its area is 400 cm square 2) Calculate the radius of the circle whose circumference is 400 cm. 3) Calculate circle circumference if its area is 400 cm square 4) Calculate the circle's area if perimeter 400 cm.
14. Triangular prism
Calculate the surface of a triangular prism 10 cm high, the base of which is a triangle with sides 6 cm 8 cm and 8 cm
15. Square prism
Calculate the volume of a square prism of high 2 dm wherein the base is: rectangle with sides 17 cm and 1.3 dm
The quadrangular prism has a volume 648 cm3. Trapezoid which is its base has the dimensions bases: a = 10 cm, c = 5 and height v = 6 cm. What is the height of the prism?
17. Magic belt
The magic rectangular belt has the property that whenever its owner wants something, the length of the belt is reduced to 1/2 and the width to 1/3. After three such wishes, the belt had a content area 4 cm2. What was its original length if the original wid
18. 30-gon
At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
19. Map scale
On a 1:1000 scale map is a rectangular land of 4.2 cm and 5.8 cm. What is the area of this land in square meters?
20. Megapascals
What is the area of crosssection of the piston, if the force of 300 kN produces a pressure of 5 MPa?

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