Examples of area of plane shapes - page 23

1. The perimeter The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX?
2. Rectangular triangle The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle?
3. Equilateral triangle Calculate the area of an equilateral triangle with circumference 72cm.
4. Sand path How many m3 of sand is needed to fill the 1.5m wide path around a rectangular flowerbed of 8m and 14m if the sand layer is 6cm high?
5. Two rectangles I cut out two rectangles with 54 cm², 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together I get a rectangle with an area of 144 cm2. What dimensions can this large rectangle have? Write all options. Explain your calcu
6. Coordinate axes Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y.
7. Diameter to area Find the area of a circle whose diameter is 26cm.
8. 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.
9. Enlarged rectangle The rectangle with dimensions of 8 cm and 12 cm is enlarged in a ratio of 5:4. What are the circumference and the area of the enlarged rectangle?
10. Square prism Calculate the volume of a foursided prism 2 dm high, the base is a trapezoid with bases 12 cm, 6 cm, height of 4 cm and 5 cm long arms.
11. Base of house Calculate the volume of the bases of a square house, if the base depth is 1.2 m, the width is 40 cm and their outer circumference is 40.7 m.
12. Diagonal to area Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
13. 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?
14. Triangular prism Calculate the surface of a regular triangular prism with a bottom edge 8 of a length of 5 meters and an appropriate height of 60 meters and prism height is 1 whole 4 meters.
15. Area of garden If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increas
16. Annual rainfall The average annual rainfall is 686 mm. How many liters will fall on the 1-hectare field?
17. The sides 2 The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
18. Diamond diagonals Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
19. Nonagon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
20. 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.

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